var bibbase_data = {"data":"<img src=\"//bibbase.org/img/ajax-loader.gif\" id=\"spinner\"\n  style=\"display: none;\" alt=\"Loading..\" />\n\n<div id=\"bibbase\">\n\n  <script type=\"text/javascript\">\n    var bibbase = {\n      params: {\"bib\":\"https://drive.google.com/uc?export=download&id=1NEXsxwRAx2CWt43v0y0jyZdP1LdOS_xF\",\"jsonp\":\"1\",\"authorFirst\":\"1\",\"sort\":\"-year\",\"theme\":\"side\",\"filter\":\"keywords:algebra\\\\b\",\"host\":\"bibbase.org\"},\n      data: [{\"bibtype\":\"article\",\"type\":\"article\",\"title\":\"X-inner automorphisms of semi-commutative quantum algebras\",\"author\":[{\"propositions\":[],\"lastnames\":[\"Bergen\"],\"firstnames\":[\"Jeffrey\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Wilson\"],\"firstnames\":[\"Mark\",\"C.\"],\"suffixes\":[]}],\"journal\":\"Journal of Algebra\",\"volume\":\"220\",\"number\":\"1\",\"pages\":\"152-173\",\"year\":\"1999\",\"publisher\":\"Academic Press\",\"keywords\":\"algebra\",\"url_paper\":\"https://www.sciencedirect.com/science/article/pii/S0021869399979279\",\"abstract\":\"Many important quantum algebras such as quantum symplectic space, quantum euclidean space, quantum matrices, $q$-analogs of the Heisenberg algebra and the quantum Weyl algebra are semi-commutative. In addition, enveloping algebras $U(L_+)$ of even Lie color algebras are also semi-commutative. In this paper, we generalize work of Montgomery and examine the X-inner automorphisms of such algebras. The theorems and examples in our paper show that for algebras $R$ of this type, the non-identity X-inner automorphisms of $R$ tend to have infinite order. Thus if $G$ is a finite group of automorphisms of $R$, then the action of $G$ will be X-outer and this immediately gives useful information about crossed products $R∗_t G$.\",\"bibtex\":\"@article{bergen1999x,\\n  title={X-inner automorphisms of semi-commutative quantum algebras},\\n  author={Bergen, Jeffrey and Wilson, Mark C.},\\n  journal={Journal of Algebra},\\n  volume={220},\\n  number={1},\\n  pages={152-173},\\n  year={1999},\\n  publisher={Academic Press},\\n  keywords={algebra},\\n  url_Paper={https://www.sciencedirect.com/science/article/pii/S0021869399979279},\\n  abstract={Many important quantum algebras such as quantum symplectic space,\\nquantum euclidean space, quantum matrices, $q$-analogs of the Heisenberg\\nalgebra and the quantum Weyl algebra are semi-commutative. In addition,\\nenveloping algebras $U(L_+)$ of even Lie color algebras are also\\nsemi-commutative. In this paper, we generalize work of Montgomery and\\nexamine the X-inner automorphisms of such algebras. The theorems and\\nexamples in our paper show that for algebras $R$ of this type, the\\nnon-identity X-inner automorphisms of  $R$ tend to have infinite order.\\nThus if $G$ is a finite group of automorphisms of $R$, then the action\\nof $G$ will be X-outer and this immediately gives useful information\\nabout crossed products  $R∗_t G$.}\\n}\\n\\n\",\"author_short\":[\"Bergen, J.\",\"Wilson, M. C.\"],\"key\":\"bergen1999x\",\"id\":\"bergen1999x\",\"bibbaseid\":\"bergen-wilson-xinnerautomorphismsofsemicommutativequantumalgebras-1999\",\"role\":\"author\",\"urls\":{\" paper\":\"https://www.sciencedirect.com/science/article/pii/S0021869399979279\"},\"keyword\":[\"algebra\"],\"metadata\":{\"authorlinks\":{\"wilson, m\":\"https://markcwilson.site/Research/Outputs/papers.html\"}},\"html\":\"\"},{\"bibtype\":\"article\",\"type\":\"article\",\"title\":\"Associative algebras satisfying a semigroup identity\",\"author\":[{\"propositions\":[],\"lastnames\":[\"Riley\"],\"firstnames\":[\"D.M.\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Wilson\"],\"firstnames\":[\"Mark\",\"C.\"],\"suffixes\":[]}],\"journal\":\"Glasgow Mathematical Journal\",\"volume\":\"41\",\"number\":\"3\",\"pages\":\"453-462\",\"year\":\"1999\",\"publisher\":\"Cambridge University Press\",\"keywords\":\"algebra\",\"url_paper\":\"https://www.cambridge.org/core/journals/glasgow-mathematical-journal/article/associative-algebras-satisfying-a-semigroup-identity/89A9FE38678C0635AE59E0B3286291CA\",\"abstract\":\"Denote by $(R,·)$ the multiplicative semigroup of an associative algebra $R$ over an infinite field, and let $(R,∘)$ represent $R$ when viewed as a semigroup via the circle operation $x∘ y=x+y+xy$. In this paper we characterize the existence of an identity in these semigroups in terms of the Lie structure of $R$. Namely, we prove that the following conditions on $R$ are equivalent: the semigroup $(R,∘)$ satisfies an identity; the semigroup $(R,·)$ satisfies a reduced identity; and, the associated Lie algebra of $R$ satisfies the Engel condition. When $R$ is finitely generated these conditions are each equivalent to $R$ being upper Lie nilpotent.\",\"bibtex\":\"@article{riley1999associative,\\n  title={Associative algebras satisfying a semigroup identity},\\n  author={Riley, D.M. and Wilson, Mark C.},\\n  journal={Glasgow Mathematical Journal},\\n  volume={41},\\n  number={3},\\n  pages={453-462},\\n  year={1999},\\n  publisher={Cambridge University Press},\\n  keywords={algebra},\\n  url_Paper={https://www.cambridge.org/core/journals/glasgow-mathematical-journal/article/associative-algebras-satisfying-a-semigroup-identity/89A9FE38678C0635AE59E0B3286291CA},\\n  abstract={Denote by $(R,\\\\cdot)$ the multiplicative semigroup of an associative\\nalgebra $R$ over an infinite field, and let $(R,\\\\circ)$ represent $R$\\nwhen viewed as a semigroup via the circle operation $x\\\\circ y=x+y+xy$.\\nIn this paper we characterize the existence of an identity in these\\nsemigroups in terms of the Lie structure of $R$. Namely, we prove that\\nthe following conditions on $R$ are equivalent: the semigroup\\n$(R,\\\\circ)$ satisfies an identity; the semigroup $(R,\\\\cdot)$ satisfies a\\nreduced identity; and, the associated Lie algebra of $R$ satisfies the\\nEngel condition. When $R$ is finitely generated these conditions are\\neach equivalent to $R$ being upper Lie nilpotent.}\\n}\\n\\n\",\"author_short\":[\"Riley, D.\",\"Wilson, M. C.\"],\"key\":\"riley1999associative-1\",\"id\":\"riley1999associative-1\",\"bibbaseid\":\"riley-wilson-associativealgebrassatisfyingasemigroupidentity-1999\",\"role\":\"author\",\"urls\":{\" paper\":\"https://www.cambridge.org/core/journals/glasgow-mathematical-journal/article/associative-algebras-satisfying-a-semigroup-identity/89A9FE38678C0635AE59E0B3286291CA\"},\"keyword\":[\"algebra\"],\"metadata\":{\"authorlinks\":{\"wilson, m\":\"https://markcwilson.site/Research/Outputs/papers.html\"}},\"html\":\"\"},{\"bibtype\":\"article\",\"type\":\"article\",\"title\":\"Group algebras and enveloping algebras with nonmatrix and semigroup identities\",\"author\":[{\"propositions\":[],\"lastnames\":[\"Riley\"],\"firstnames\":[\"D.M.\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Wilson\"],\"firstnames\":[\"Mark\",\"C.\"],\"suffixes\":[]}],\"journal\":\"Communications in Algebra\",\"volume\":\"27\",\"number\":\"7\",\"pages\":\"3545-3556\",\"year\":\"1999\",\"publisher\":\"Taylor & Francis\",\"keywords\":\"algebra\",\"url_paper\":\"https://www.tandfonline.com/doi/abs/10.1080/00927879908826645\",\"abstract\":\"Let $K$ be a field of characteristic $p>0$. Denote by $ω(R)$ the augmentation ideal of either a group algebra $R=K[G]$ or a restricted enveloping algebra $R=u(L)$ over $K$. We first characterize those $R$ for which $ω(R)$ satisfies a polynomial identity not satisfied by the algebra of all $2× 2$ matrices over $K$. Then, we examine those $R$ for which $ω(R)$ satisfies a semigroup identity (that is, a polynomial identity which can be written as the difference of two monomials).\",\"bibtex\":\"@article{riley1999group,\\n  title={Group algebras and enveloping algebras with nonmatrix and semigroup identities},\\n  author={Riley, D.M. and Wilson, Mark C.},\\n  journal={Communications in Algebra},\\n  volume={27},\\n  number={7},\\n  pages={3545-3556},\\n  year={1999},\\n  publisher={Taylor \\\\& Francis},\\n  keywords={algebra},\\n  url_Paper={https://www.tandfonline.com/doi/abs/10.1080/00927879908826645},\\n  abstract={Let $K$ be a field of characteristic $p>0$.  Denote by $\\\\omega(R)$ the\\naugmentation ideal of either a group algebra $R=K[G]$ or a restricted\\nenveloping algebra $R=u(L)$ over $K$.   We first characterize those $R$\\nfor which $\\\\omega(R)$ satisfies a polynomial identity not satisfied by\\nthe algebra of all $2\\\\times 2$ matrices over $K$. Then, we examine those\\n$R$ for which $\\\\omega(R)$ satisfies a semigroup identity (that is, a\\npolynomial identity which can be written as the difference of two\\nmonomials).}\\n}\\n\\n\",\"author_short\":[\"Riley, D.\",\"Wilson, M. C.\"],\"key\":\"riley1999group\",\"id\":\"riley1999group\",\"bibbaseid\":\"riley-wilson-groupalgebrasandenvelopingalgebraswithnonmatrixandsemigroupidentities-1999\",\"role\":\"author\",\"urls\":{\" paper\":\"https://www.tandfonline.com/doi/abs/10.1080/00927879908826645\"},\"keyword\":[\"algebra\"],\"metadata\":{\"authorlinks\":{\"wilson, m\":\"https://markcwilson.site/Research/Outputs/papers.html\"}},\"html\":\"\"},{\"bibtype\":\"article\",\"type\":\"article\",\"title\":\"Associative rings satisfying the Engel condition\",\"author\":[{\"propositions\":[],\"lastnames\":[\"Riley\"],\"firstnames\":[\"D.M.\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Wilson\"],\"firstnames\":[\"Mark\",\"C.\"],\"suffixes\":[]}],\"journal\":\"Proceedings of the American Mathematical Society\",\"volume\":\"127\",\"number\":\"4\",\"pages\":\"973-976\",\"year\":\"1999\",\"keywords\":\"algebra\",\"url_paper\":\"https://www.ams.org/journals/proc/1999-127-04/S0002-9939-99-04643-2/S0002-9939-99-04643-2.pdf\",\"abstract\":\"Let $C$ be a commutative ring, and let $R$ be an associative $C$-algebra generated by elements $\\\\{x_1,…,x_d\\\\}$. We show that if $R$ satisfies the Engel condition of degree $n$ then $R$ is upper Lie nilpotent of class bounded by a function that depends only on $d$ and $n$. We deduce that the Engel condition in an arbitrary associative ring is inherited by its group of units, and implies a semigroup identity.\",\"bibtex\":\"@article{riley1999associative,\\n  title={Associative rings satisfying the Engel condition},\\n  author={Riley, D.M. and Wilson, Mark C.},\\n  journal={Proceedings of the American Mathematical Society},\\n  volume={127},\\n  number={4},\\n  pages={973-976},\\n  year={1999},\\n  keywords={algebra},\\n  url_Paper={https://www.ams.org/journals/proc/1999-127-04/S0002-9939-99-04643-2/S0002-9939-99-04643-2.pdf},\\n  abstract={Let $C$ be a commutative ring, and let $R$ be an associative $C$-algebra\\ngenerated by elements $\\\\{x_1,\\\\ldots,x_d\\\\}$. We show that if $R$\\nsatisfies the Engel condition of degree $n$ then $R$ is upper Lie\\nnilpotent of class bounded by a function that depends only on $d$ and\\n$n$. We deduce that the Engel condition in an arbitrary associative ring\\nis inherited by its group of units, and implies a semigroup identity.}\\n}\\n\\n\",\"author_short\":[\"Riley, D.\",\"Wilson, M. C.\"],\"key\":\"riley1999associative\",\"id\":\"riley1999associative\",\"bibbaseid\":\"riley-wilson-associativeringssatisfyingtheengelcondition-1999\",\"role\":\"author\",\"urls\":{\" paper\":\"https://www.ams.org/journals/proc/1999-127-04/S0002-9939-99-04643-2/S0002-9939-99-04643-2.pdf\"},\"keyword\":[\"algebra\"],\"metadata\":{\"authorlinks\":{\"wilson, m\":\"https://markcwilson.site/Research/Outputs/papers.html\"}},\"html\":\"\"},{\"bibtype\":\"article\",\"type\":\"article\",\"title\":\"Primitive ideals in Hopf algebra extensions\",\"author\":[{\"propositions\":[],\"lastnames\":[\"Wilson\"],\"firstnames\":[\"Mark\",\"C.\"],\"suffixes\":[]}],\"journal\":\"arXiv preprint math/9808122\",\"year\":\"1998\",\"keywords\":\"algebra\",\"url_paper\":\"https://arxiv.org/pdf/math/9808122.pdf\",\"abstract\":\"My last paper in algebra, never published formally.\",\"bibtex\":\"@article{wilson1998primitive,\\n  title={Primitive ideals in Hopf algebra extensions},\\n  author={Wilson, Mark C.},\\n  journal={arXiv preprint math/9808122},\\n  year={1998},\\n  keywords={algebra},\\n  url_Paper={https://arxiv.org/pdf/math/9808122.pdf},\\n  abstract={My last paper in algebra, never published formally.}\\n}\\n\\n\",\"author_short\":[\"Wilson, M. C.\"],\"key\":\"wilson1998primitive\",\"id\":\"wilson1998primitive\",\"bibbaseid\":\"wilson-primitiveidealsinhopfalgebraextensions-1998\",\"role\":\"author\",\"urls\":{\" paper\":\"https://arxiv.org/pdf/math/9808122.pdf\"},\"keyword\":[\"algebra\"],\"metadata\":{\"authorlinks\":{\"wilson, m\":\"https://markcwilson.site/Research/Outputs/papers.html\"}},\"html\":\"\"},{\"bibtype\":\"article\",\"type\":\"article\",\"title\":\"Bell's primeness criterion and the simple Lie superalgebras\",\"author\":[{\"propositions\":[],\"lastnames\":[\"Wilson\"],\"firstnames\":[\"Mark\",\"C.\"],\"suffixes\":[]}],\"journal\":\"Journal of Pure and Applied Algebra\",\"volume\":\"133\",\"number\":\"1-2\",\"pages\":\"241-260\",\"year\":\"1998\",\"publisher\":\"North-Holland\",\"keywords\":\"algebra\",\"url_paper\":\"https://www.sciencedirect.com/science/article/pii/S0022404997001990\",\"abstract\":\"We determine all finite-dimensional simple Lie superalgebras $L$ such that $U(L)$ satisfies a primeness criterion due to Bell. Some open problems related to primeness of enveloping algebras are listed.\",\"bibtex\":\"@article{wilson1998bell,\\n  title={Bell's primeness criterion and the simple Lie superalgebras},\\n  author={Wilson, Mark C.},\\n  journal={Journal of Pure and Applied Algebra},\\n  volume={133},\\n  number={1-2},\\n  pages={241-260},\\n  year={1998},\\n  publisher={North-Holland},\\n  keywords={algebra},\\n  url_Paper={https://www.sciencedirect.com/science/article/pii/S0022404997001990},\\n  abstract={We determine all finite-dimensional simple Lie superalgebras $L$ such\\nthat $U(L)$ satisfies a primeness criterion due to Bell. Some open\\nproblems related to primeness of enveloping algebras are listed.}\\n}\\n\\n\",\"author_short\":[\"Wilson, M. C.\"],\"key\":\"wilson1998bell\",\"id\":\"wilson1998bell\",\"bibbaseid\":\"wilson-bellsprimenesscriterionandthesimpleliesuperalgebras-1998\",\"role\":\"author\",\"urls\":{\" paper\":\"https://www.sciencedirect.com/science/article/pii/S0022404997001990\"},\"keyword\":[\"algebra\"],\"metadata\":{\"authorlinks\":{\"wilson, m\":\"https://markcwilson.site/Research/Outputs/papers.html\"}},\"html\":\"\"},{\"bibtype\":\"article\",\"type\":\"article\",\"title\":\"Primeness of the enveloping algebra of the special Lie superalgebras\",\"author\":[{\"propositions\":[],\"lastnames\":[\"Wilson\"],\"firstnames\":[\"Mark\",\"C.\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Pritchard\"],\"firstnames\":[\"Geoffrey\"],\"suffixes\":[]}],\"journal\":\"Archiv der Mathematik\",\"volume\":\"70\",\"number\":\"3\",\"pages\":\"187-196\",\"year\":\"1998\",\"publisher\":\"Birkhäuser Verlag\",\"keywords\":\"algebra\",\"url_paper\":\"https://link.springer.com/article/10.1007/s000130050183\",\"abstract\":\"A primeness criterion due to Bell is shown to apply to the universal enveloping algebra of the Cartan type Lie superalgebras $S(V)$ and $\\\\widetilde{S}(V;t)$ when $\\\\dim V$ is even. On the other hand, if $\\\\dim V$ is odd then $U(S(V))$ is never semiprime.\",\"bibtex\":\"@article{wilson1998primeness,\\n  title={Primeness of the enveloping algebra of the special Lie superalgebras},\\n  author={Wilson, Mark C. and Pritchard, Geoffrey},\\n  journal={Archiv der Mathematik},\\n  volume={70},\\n  number={3},\\n  pages={187-196},\\n  year={1998},\\n  publisher={Birkh{\\\\\\\"a}user Verlag},\\n  keywords={algebra},\\n  url_Paper={https://link.springer.com/article/10.1007/s000130050183},\\n  abstract={A primeness criterion due to Bell is shown to apply to the universal\\nenveloping algebra of the Cartan type Lie superalgebras $S(V)$ and\\n$\\\\widetilde{S}(V;t)$ when $\\\\dim V$ is even. On the other hand, if $\\\\dim\\nV$ is odd then $U(S(V))$ is never semiprime.}\\n}\\n\\n\",\"author_short\":[\"Wilson, M. C.\",\"Pritchard, G.\"],\"key\":\"wilson1998primeness\",\"id\":\"wilson1998primeness\",\"bibbaseid\":\"wilson-pritchard-primenessoftheenvelopingalgebraofthespecialliesuperalgebras-1998\",\"role\":\"author\",\"urls\":{\" paper\":\"https://link.springer.com/article/10.1007/s000130050183\"},\"keyword\":[\"algebra\"],\"metadata\":{\"authorlinks\":{\"wilson, m\":\"https://markcwilson.site/Research/Outputs/papers.html\"}},\"html\":\"\"},{\"bibtype\":\"article\",\"type\":\"article\",\"title\":\"Crossed products of restricted enveloping algebras\",\"author\":[{\"propositions\":[],\"lastnames\":[\"Wilson\"],\"firstnames\":[\"Mark\",\"C.\"],\"suffixes\":[]}],\"journal\":\"Communications in Algebra\",\"volume\":\"25\",\"number\":\"2\",\"pages\":\"487-496\",\"year\":\"1997\",\"publisher\":\"Taylor & Francis\",\"keywords\":\"algebra\",\"url_paper\":\"https://www.tandfonline.com/doi/abs/10.1080/00927879708825868\",\"abstract\":\"Let $K$ be a field of characteristic $p>0$, let $L$ be a restricted Lie algebra and let $R$ be an associative $K$-algebra. It is shown that the various constructions in the literature of crossed product of $R$ with $u(L)$ are equivalent. We calculate explicit formulae relating the parameters involved and obtain a formula which hints at a noncommutative version of the Bell polynomials.\",\"bibtex\":\"@article{wilson1997crossed,\\n  title={Crossed products of restricted enveloping algebras},\\n  author={Wilson, Mark C.},\\n  journal={Communications in Algebra},\\n  volume={25},\\n  number={2},\\n  pages={487-496},\\n  year={1997},\\n  publisher={Taylor \\\\& Francis},\\n  keywords={algebra},\\n  url_Paper={https://www.tandfonline.com/doi/abs/10.1080/00927879708825868},\\n  abstract={Let $K$ be a field of characteristic $p>0$, let $L$ be a restricted Lie\\nalgebra and let $R$ be an associative $K$-algebra. It is shown that the\\nvarious constructions in the literature of crossed product of  $R$ with\\n$u(L)$ are equivalent. We calculate explicit formulae relating the\\nparameters involved and obtain a formula which hints at a noncommutative\\nversion of the Bell polynomials.}\\n}\\n\\n\",\"author_short\":[\"Wilson, M. C.\"],\"key\":\"wilson1997crossed\",\"id\":\"wilson1997crossed\",\"bibbaseid\":\"wilson-crossedproductsofrestrictedenvelopingalgebras-1997\",\"role\":\"author\",\"urls\":{\" paper\":\"https://www.tandfonline.com/doi/abs/10.1080/00927879708825868\"},\"keyword\":[\"algebra\"],\"metadata\":{\"authorlinks\":{\"wilson, m\":\"https://markcwilson.site/Research/Outputs/papers.html\"}},\"html\":\"\"},{\"bibtype\":\"article\",\"type\":\"article\",\"title\":\"Bell's primeness criterion for $W(2n+ 1)$\",\"author\":[{\"propositions\":[],\"lastnames\":[\"Wilson\"],\"firstnames\":[\"Mark\",\"C.\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Pritchard\"],\"firstnames\":[\"Geoffrey\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Wood\"],\"firstnames\":[\"David\",\"H.\"],\"suffixes\":[]}],\"journal\":\"Experimental Mathematics\",\"volume\":\"6\",\"number\":\"1\",\"pages\":\"77-85\",\"year\":\"1997\",\"publisher\":\"Taylor & Francis Group\",\"keywords\":\"algebra\",\"url_paper\":\"https://doi.org/10.1080/10586458.1997.10504352\",\"abstract\":\"On the basis of experimental work involving matrix computations, we conjecture that a criterion due to Bell for primeness of the universal enveloping algebra of a Lie superalgebra applies to the Cartan type Lie superalgebras $W(n)$ for $n=3$ but does not apply for odd $n≥ 5$. The experiments lead to a rigorous proof, which we present.\",\"bibtex\":\"@article{wilson1997bell,\\n  title={Bell's primeness criterion for $W(2n+ 1)$},\\n  author={Wilson, Mark C. and Pritchard, Geoffrey and Wood, David H.},\\n  journal={Experimental Mathematics},\\n  volume={6},\\n  number={1},\\n  pages={77-85},\\n  year={1997},\\n  publisher={Taylor \\\\& Francis Group},\\n  keywords={algebra},\\n  url_Paper={https://doi.org/10.1080/10586458.1997.10504352},\\n  abstract={On the basis of experimental work involving matrix computations, we\\nconjecture that a criterion due to Bell for primeness of the universal\\nenveloping algebra of a Lie superalgebra applies to the Cartan type Lie\\nsuperalgebras $W(n)$ for $n=3$ but does not apply for odd $n\\\\geq 5$. The\\nexperiments lead to a rigorous proof, which we present.}\\n}\\n\\n\",\"author_short\":[\"Wilson, M. C.\",\"Pritchard, G.\",\"Wood, D. H.\"],\"key\":\"wilson1997bell\",\"id\":\"wilson1997bell\",\"bibbaseid\":\"wilson-pritchard-wood-bellsprimenesscriterionforw2n1-1997\",\"role\":\"author\",\"urls\":{\" paper\":\"https://doi.org/10.1080/10586458.1997.10504352\"},\"keyword\":[\"algebra\"],\"metadata\":{\"authorlinks\":{\"wilson, m\":\"https://markcwilson.site/Research/Outputs/papers.html\"}},\"html\":\"\"},{\"bibtype\":\"article\",\"type\":\"article\",\"title\":\"Primeness of the enveloping algebra of Hamiltonian superalgebras\",\"author\":[{\"propositions\":[],\"lastnames\":[\"Wilson\"],\"firstnames\":[\"Mark\",\"C.\"],\"suffixes\":[]}],\"journal\":\"Bulletin of the Australian Mathematical Society\",\"volume\":\"56\",\"number\":\"3\",\"pages\":\"483-488\",\"year\":\"1997\",\"publisher\":\"Cambridge University Press\",\"keywords\":\"algebra\",\"url_paper\":\"https://www.cambridge.org/core/journals/bulletin-of-the-australian-mathematical-society/article/primeness-of-the-enveloping-algebra-of-hamiltonian-superalgebras/A643AA62E4FAC8098924C1DE44E463C8\",\"abstract\":\"In 1990 Allen Bell presented a sufficient condition for the primeness of the universal enveloping algebra of a Lie superalgebra. Let $Q$ be a nonsingular bilinear form on a finite-dimensional vector space over a field of characteristic zero. In this paper we show that Bell's criterion applies to the Hamiltonian Cartan type superalgebras determined by $Q$, and hence obtain some new prime noetherian rings.\",\"bibtex\":\"@article{wilson1997primeness,\\n  title={Primeness of the enveloping algebra of Hamiltonian superalgebras},\\n  author={Wilson, Mark C.},\\n  journal={Bulletin of the Australian Mathematical Society},\\n  volume={56},\\n  number={3},\\n  pages={483-488},\\n  year={1997},\\n  publisher={Cambridge University Press},\\n  keywords={algebra},\\n  url_Paper={https://www.cambridge.org/core/journals/bulletin-of-the-australian-mathematical-society/article/primeness-of-the-enveloping-algebra-of-hamiltonian-superalgebras/A643AA62E4FAC8098924C1DE44E463C8},\\n  abstract={In 1990 Allen Bell presented a sufficient condition for the primeness of\\nthe universal enveloping algebra of a Lie superalgebra. Let $Q$ be a\\nnonsingular bilinear form on a finite-dimensional vector space over a\\nfield of characteristic zero. In this paper we show that Bell's\\ncriterion applies to the Hamiltonian Cartan type superalgebras\\ndetermined by $Q$, and hence obtain some new prime noetherian rings.}\\n}\\n\\n\",\"author_short\":[\"Wilson, M. C.\"],\"key\":\"wilson1997primeness\",\"id\":\"wilson1997primeness\",\"bibbaseid\":\"wilson-primenessoftheenvelopingalgebraofhamiltoniansuperalgebras-1997\",\"role\":\"author\",\"urls\":{\" paper\":\"https://www.cambridge.org/core/journals/bulletin-of-the-australian-mathematical-society/article/primeness-of-the-enveloping-algebra-of-hamiltonian-superalgebras/A643AA62E4FAC8098924C1DE44E463C8\"},\"keyword\":[\"algebra\"],\"metadata\":{\"authorlinks\":{\"wilson, m\":\"https://markcwilson.site/Research/Outputs/papers.html\"}},\"html\":\"\"},{\"bibtype\":\"article\",\"type\":\"article\",\"title\":\"Primeness of the enveloping algebra of a Cartan type Lie superalgebra\",\"author\":[{\"propositions\":[],\"lastnames\":[\"Wilson\"],\"firstnames\":[\"Mark\",\"C.\"],\"suffixes\":[]}],\"journal\":\"Proceedings of the American Mathematical Society\",\"volume\":\"124\",\"number\":\"2\",\"pages\":\"383-387\",\"year\":\"1996\",\"keywords\":\"algebra\",\"url_paper\":\"\",\"abstract\":\"We show that a primeness criterion for enveloping algebras of Lie superalgebras discovered by Bell is applicable to the Cartan type Lie superalgebras $W(n)$, $n$ even. Other algebras are considered but there are no definitive answers in these cases.\",\"bibtex\":\"@article{wilson1996primeness,\\n  title={Primeness of the enveloping algebra of a Cartan type Lie superalgebra},\\n  author={Wilson, Mark C.},\\n  journal={Proceedings of the American Mathematical Society},\\n  volume={124},\\n  number={2},\\n  pages={383-387},\\n  year={1996},\\n  keywords={algebra},\\n  url_Paper={},\\n  abstract={We show that a primeness criterion for enveloping algebras of Lie\\nsuperalgebras discovered by Bell is applicable to the Cartan type Lie\\nsuperalgebras $W(n)$, $n$ even. Other algebras are considered but there\\nare no definitive answers in these cases.}\\n}\\n\\n\\n\\n\",\"author_short\":[\"Wilson, M. C.\"],\"key\":\"wilson1996primeness\",\"id\":\"wilson1996primeness\",\"bibbaseid\":\"wilson-primenessoftheenvelopingalgebraofacartantypeliesuperalgebra-1996\",\"role\":\"author\",\"urls\":{\" paper\":\"https://drive.google.com/uc?export=download&id=1NEXsxwRAx2CWt43v0y0jyZdP1LdOS_xF\"},\"keyword\":[\"algebra\"],\"metadata\":{\"authorlinks\":{\"wilson, m\":\"https://markcwilson.site/Research/Outputs/papers.html\"}},\"html\":\"\"},{\"bibtype\":\"article\",\"type\":\"article\",\"title\":\"Delta methods in enveloping algebras of Lie color algebras\",\"author\":[{\"propositions\":[],\"lastnames\":[\"Wilson\"],\"firstnames\":[\"Mark\",\"C.\"],\"suffixes\":[]}],\"journal\":\"Journal of Algebra\",\"volume\":\"175\",\"number\":\"2\",\"pages\":\"661-696\",\"year\":\"1995\",\"publisher\":\"Academic Press\",\"keywords\":\"algebra\",\"url_paper\":\"https://www.sciencedirect.com/science/article/pii/S0021869385712070\",\"abstract\":\"In recent papers J. Bergen and D.S. Passman have applied so-called `Delta methods' to enveloping algebras of Lie superalgebras. This paper generalizes their results to the class of Lie colour algebras. The methods and results in this paper are very similar to those of Bergen and Passman, and many of their proofs generalize easily. However, at some points there are serious difficulties to overcome. The results obtained show that if $L$ is a Lie colour algebra then the join of all finite-dimensional ideals of $L$ controls certain properties of the universal enveloping algebras $U(L)$. Specifically, we consider primeness, semiprimeness, constants, semi-invariants, almost constants, faithfulness of the adjoint action, the centre, almost centralizers and the central closure.\",\"bibtex\":\"@article{wilson1995delta,\\n  title={Delta methods in enveloping algebras of Lie color algebras},\\n  author={Wilson, Mark C.},\\n  journal={Journal of Algebra},\\n  volume={175},\\n  number={2},\\n  pages={661-696},\\n  year={1995},\\n  publisher={Academic Press},\\n  keywords={algebra},\\n  url_Paper={https://www.sciencedirect.com/science/article/pii/S0021869385712070},\\n  abstract={In recent papers J. Bergen and D.S. Passman have applied so-called\\n`Delta methods' to enveloping algebras of Lie superalgebras. This paper\\ngeneralizes their results to the class of Lie colour algebras. The\\nmethods and results in this paper are very similar to those of Bergen\\nand Passman, and many of their proofs generalize easily. However, at\\nsome points there are serious difficulties to overcome. The results\\nobtained show that if $L$ is a Lie colour algebra then the join of all\\nfinite-dimensional ideals of  $L$ controls certain properties of the\\nuniversal enveloping algebras  $U(L)$. Specifically, we consider\\nprimeness, semiprimeness, constants, semi-invariants, almost constants,\\nfaithfulness of the adjoint action, the centre, almost centralizers and\\nthe central closure.}\\n}\\n\\n\",\"author_short\":[\"Wilson, M. C.\"],\"key\":\"wilson1995delta\",\"id\":\"wilson1995delta\",\"bibbaseid\":\"wilson-deltamethodsinenvelopingalgebrasofliecoloralgebras-1995\",\"role\":\"author\",\"urls\":{\" paper\":\"https://www.sciencedirect.com/science/article/pii/S0021869385712070\"},\"keyword\":[\"algebra\"],\"metadata\":{\"authorlinks\":{\"wilson, m\":\"https://markcwilson.site/Research/Outputs/papers.html\"}},\"html\":\"\"}],\n      metadata: {\"owner\":\"wilson, m\",\"authorlinks\":{\"wilson, m\":\"https://markcwilson.site/Research/Outputs/papers.html\"}},\n      ownerID: \"2SHj7sd7JeFWTntxS\"\n    };\n  </script>\n\n  <script type=\"text/javascript\">\n  var site$;\n  if (typeof $ != 'undefined') {\n    console.log('existing jquery: storing and then restoring');\n    site$ = $;\n    $ = null;\n  }\n  </script>\n\n  <script src=\"https://ajax.googleapis.com/ajax/libs/jquery/2.2.4/jquery.min.js\">\n  </script>\n  <script type=\"text/javascript\">\n  if (site$) {\n    console.log('existing jquery: avoiding conflict and restoring');\n    bb$ = $.noConflict(true);\n    $ = site$;\n  } else {\n    bb$ = $;\n  }\n  </script>\n\n  <script src=\"//bibbase.org/js/bibbase.min.js\"\n          type=\"text/javascript\">\n  </script>\n\n  <script type=\"text/javascript\"\n          src=\"https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/MathJax.js?config=TeX-AMS-MML_HTMLorMML\">\n  </script>\n  <script type=\"text/x-mathjax-config\">\n    MathJax.Hub.Config({tex2jax: {inlineMath: [['$','$'], ['\\\\(','\\\\)']]},\n                        skipTags: [\"body\"],\n                        processClass: \"bibbase_paper\"});\n  </script>\n\n  <style>\n  @media print {\n    .dontprint {\n        display: none !important;\n    }\n\n  .bibbase_group {\n    background-color: #E0E0E0;\n    font-style: italic;\n    font-size: larger;\n    text-shadow: 0px 0px 3px #FFFFFF;\n    border-radius: 4px 4px 4px 4px;\n    -moz-border-radius: 4px 4px 4px 4px;\n    -webkit-border-radius: 4px;\n    padding: 5px 40px 5px;\n    margin-top: 10px;\n    margin-bottom: 5px;\n    cursor: pointer;\n  }\n\n  .bibbase_paper {\n    margin-bottom: 5px;\n  }\n\n  }\n  </style>\n\n  \n  <div style=\"float: right; margin-right: 10px; margin-top: 10px; text-align: right; font-size: 12px\">\n    generated by\n    <a href=\"//bibbase.org\"\n       onclick=\"trackOutboundLink('bibbase', 'logo clicked', window.location.href, '//bibbase.org'); return false;\">\n      <img src=\"//bibbase.org/img/logo.svg\"\n           style=\"vertical-align: middle; margin-left: 3px; height: 16px;\"/\n           alt=\"bibbase.org\"\n           title=\"BibBase – The easiest way to maintain your publications page.\"\n        ></a>\n    \n  </div>\n  \n\n  <div id=\"bibbase_header\" class=\"dontprint\" style=\"\">\n\n    <ul class=\"nav nav-pills\" style=\"margin: 0px;\">\n\n      <li class=\"dropdown\" id=\"groupby_dropdown\">\n      <a class=\"dropdown-toggle\"\n         data-toggle=\"dropdown\"\n         href=\"#\">\n          Group by\n          <b class=\"caret\"></b>\n      </a>\n      <ul class=\"dropdown-menu\">\n        <li class=\"groupby year\"><a onclick=\"groupby('year')\">\n            Year</a>\n        </li>\n        <li class=\"groupby author\"><a onclick=\"groupby('author_short')\">\n            Author</a>\n        </li>\n        <li class=\"groupby type\"><a onclick=\"groupby('type')\">\n            Type</a>\n        </li>\n        <li class=\"groupby keyword\"><a onclick=\"groupby('keyword')\">\n            Keyword</a>\n        </li>\n        <li class=\"groupby downloads\"><a onclick=\"groupby('downloads')\">\n            Downloads</a>\n        </li>\n      </ul>\n      </li>\n\n\n      <li class=\"dropdown\" id=\"menu_dropdown\">\n      <a class=\"dropdown-toggle\"\n         data-toggle=\"dropdown\"\n         href=\"#\" alt=\"controls\">\n          <i class=\"fa fa-reorder\" alt=\"controls\"></i>\n          <b class=\"caret\"></b>\n      </a>\n      <ul class=\"dropdown-menu\">\n        <li>\n          <a onclick=\"toggleAll()\">\n            <i class=\"fa fa-chevron-down fa-fw\"></i> Expand/Collapse All\n          </a>\n        </li>\n        <li>\n          <a download=\"uc\" href=\"data:text/bibtex;base64,@article{bergen1999x,
  title={X-inner automorphisms of semi-commutative quantum algebras},
  author={Bergen, Jeffrey and Wilson, Mark C.},
  journal={Journal of Algebra},
  volume={220},
  number={1},
  pages={152-173},
  year={1999},
  publisher={Academic Press},
  keywords={algebra},
  url_Paper={https://www.sciencedirect.com/science/article/pii/S0021869399979279},
  abstract={Many important quantum algebras such as quantum symplectic space,
quantum euclidean space, quantum matrices, $q$-analogs of the Heisenberg
algebra and the quantum Weyl algebra are semi-commutative. In addition,
enveloping algebras $U(L_+)$ of even Lie color algebras are also
semi-commutative. In this paper, we generalize work of Montgomery and
examine the X-inner automorphisms of such algebras. The theorems and
examples in our paper show that for algebras $R$ of this type, the
non-identity X-inner automorphisms of  $R$ tend to have infinite order.
Thus if $G$ is a finite group of automorphisms of $R$, then the action
of $G$ will be X-outer and this immediately gives useful information
about crossed products  $R∗_t G$.}
}



@article{riley1999associative,
  title={Associative algebras satisfying a semigroup identity},
  author={Riley, D.M. and Wilson, Mark C.},
  journal={Glasgow Mathematical Journal},
  volume={41},
  number={3},
  pages={453-462},
  year={1999},
  publisher={Cambridge University Press},
  keywords={algebra},
  url_Paper={https://www.cambridge.org/core/journals/glasgow-mathematical-journal/article/associative-algebras-satisfying-a-semigroup-identity/89A9FE38678C0635AE59E0B3286291CA},
  abstract={Denote by $(R,\cdot)$ the multiplicative semigroup of an associative
algebra $R$ over an infinite field, and let $(R,\circ)$ represent $R$
when viewed as a semigroup via the circle operation $x\circ y=x+y+xy$.
In this paper we characterize the existence of an identity in these
semigroups in terms of the Lie structure of $R$. Namely, we prove that
the following conditions on $R$ are equivalent: the semigroup
$(R,\circ)$ satisfies an identity; the semigroup $(R,\cdot)$ satisfies a
reduced identity; and, the associated Lie algebra of $R$ satisfies the
Engel condition. When $R$ is finitely generated these conditions are
each equivalent to $R$ being upper Lie nilpotent.}
}



@article{riley1999group,
  title={Group algebras and enveloping algebras with nonmatrix and semigroup identities},
  author={Riley, D.M. and Wilson, Mark C.},
  journal={Communications in Algebra},
  volume={27},
  number={7},
  pages={3545-3556},
  year={1999},
  publisher={Taylor \& Francis},
  keywords={algebra},
  url_Paper={https://www.tandfonline.com/doi/abs/10.1080/00927879908826645},
  abstract={Let $K$ be a field of characteristic $p>0$.  Denote by $\omega(R)$ the
augmentation ideal of either a group algebra $R=K[G]$ or a restricted
enveloping algebra $R=u(L)$ over $K$.   We first characterize those $R$
for which $\omega(R)$ satisfies a polynomial identity not satisfied by
the algebra of all $2\times 2$ matrices over $K$. Then, we examine those
$R$ for which $\omega(R)$ satisfies a semigroup identity (that is, a
polynomial identity which can be written as the difference of two
monomials).}
}



@article{riley1999associative,
  title={Associative rings satisfying the Engel condition},
  author={Riley, D.M. and Wilson, Mark C.},
  journal={Proceedings of the American Mathematical Society},
  volume={127},
  number={4},
  pages={973-976},
  year={1999},
  keywords={algebra},
  url_Paper={https://www.ams.org/journals/proc/1999-127-04/S0002-9939-99-04643-2/S0002-9939-99-04643-2.pdf},
  abstract={Let $C$ be a commutative ring, and let $R$ be an associative $C$-algebra
generated by elements $\{x_1,\ldots,x_d\}$. We show that if $R$
satisfies the Engel condition of degree $n$ then $R$ is upper Lie
nilpotent of class bounded by a function that depends only on $d$ and
$n$. We deduce that the Engel condition in an arbitrary associative ring
is inherited by its group of units, and implies a semigroup identity.}
}



@article{wilson1998primitive,
  title={Primitive ideals in Hopf algebra extensions},
  author={Wilson, Mark C.},
  journal={arXiv preprint math/9808122},
  year={1998},
  keywords={algebra},
  url_Paper={https://arxiv.org/pdf/math/9808122.pdf},
  abstract={My last paper in algebra, never published formally.}
}



@article{wilson1998bell,
  title={Bell's primeness criterion and the simple Lie superalgebras},
  author={Wilson, Mark C.},
  journal={Journal of Pure and Applied Algebra},
  volume={133},
  number={1-2},
  pages={241-260},
  year={1998},
  publisher={North-Holland},
  keywords={algebra},
  url_Paper={https://www.sciencedirect.com/science/article/pii/S0022404997001990},
  abstract={We determine all finite-dimensional simple Lie superalgebras $L$ such
that $U(L)$ satisfies a primeness criterion due to Bell. Some open
problems related to primeness of enveloping algebras are listed.}
}



@article{wilson1998primeness,
  title={Primeness of the enveloping algebra of the special Lie superalgebras},
  author={Wilson, Mark C. and Pritchard, Geoffrey},
  journal={Archiv der Mathematik},
  volume={70},
  number={3},
  pages={187-196},
  year={1998},
  publisher={Birkh{\"a}user Verlag},
  keywords={algebra},
  url_Paper={https://link.springer.com/article/10.1007/s000130050183},
  abstract={A primeness criterion due to Bell is shown to apply to the universal
enveloping algebra of the Cartan type Lie superalgebras $S(V)$ and
$\widetilde{S}(V;t)$ when $\dim V$ is even. On the other hand, if $\dim
V$ is odd then $U(S(V))$ is never semiprime.}
}



@article{wilson1997crossed,
  title={Crossed products of restricted enveloping algebras},
  author={Wilson, Mark C.},
  journal={Communications in Algebra},
  volume={25},
  number={2},
  pages={487-496},
  year={1997},
  publisher={Taylor \& Francis},
  keywords={algebra},
  url_Paper={https://www.tandfonline.com/doi/abs/10.1080/00927879708825868},
  abstract={Let $K$ be a field of characteristic $p>0$, let $L$ be a restricted Lie
algebra and let $R$ be an associative $K$-algebra. It is shown that the
various constructions in the literature of crossed product of  $R$ with
$u(L)$ are equivalent. We calculate explicit formulae relating the
parameters involved and obtain a formula which hints at a noncommutative
version of the Bell polynomials.}
}



@article{wilson1997bell,
  title={Bell's primeness criterion for $W(2n+ 1)$},
  author={Wilson, Mark C. and Pritchard, Geoffrey and Wood, David H.},
  journal={Experimental Mathematics},
  volume={6},
  number={1},
  pages={77-85},
  year={1997},
  publisher={Taylor \& Francis Group},
  keywords={algebra},
  url_Paper={https://doi.org/10.1080/10586458.1997.10504352},
  abstract={On the basis of experimental work involving matrix computations, we
conjecture that a criterion due to Bell for primeness of the universal
enveloping algebra of a Lie superalgebra applies to the Cartan type Lie
superalgebras $W(n)$ for $n=3$ but does not apply for odd $n\geq 5$. The
experiments lead to a rigorous proof, which we present.}
}



@article{wilson1997primeness,
  title={Primeness of the enveloping algebra of Hamiltonian superalgebras},
  author={Wilson, Mark C.},
  journal={Bulletin of the Australian Mathematical Society},
  volume={56},
  number={3},
  pages={483-488},
  year={1997},
  publisher={Cambridge University Press},
  keywords={algebra},
  url_Paper={https://www.cambridge.org/core/journals/bulletin-of-the-australian-mathematical-society/article/primeness-of-the-enveloping-algebra-of-hamiltonian-superalgebras/A643AA62E4FAC8098924C1DE44E463C8},
  abstract={In 1990 Allen Bell presented a sufficient condition for the primeness of
the universal enveloping algebra of a Lie superalgebra. Let $Q$ be a
nonsingular bilinear form on a finite-dimensional vector space over a
field of characteristic zero. In this paper we show that Bell's
criterion applies to the Hamiltonian Cartan type superalgebras
determined by $Q$, and hence obtain some new prime noetherian rings.}
}



@article{wilson1996primeness,
  title={Primeness of the enveloping algebra of a Cartan type Lie superalgebra},
  author={Wilson, Mark C.},
  journal={Proceedings of the American Mathematical Society},
  volume={124},
  number={2},
  pages={383-387},
  year={1996},
  keywords={algebra},
  url_Paper={},
  abstract={We show that a primeness criterion for enveloping algebras of Lie
superalgebras discovered by Bell is applicable to the Cartan type Lie
superalgebras $W(n)$, $n$ even. Other algebras are considered but there
are no definitive answers in these cases.}
}





@article{wilson1995delta,
  title={Delta methods in enveloping algebras of Lie color algebras},
  author={Wilson, Mark C.},
  journal={Journal of Algebra},
  volume={175},
  number={2},
  pages={661-696},
  year={1995},
  publisher={Academic Press},
  keywords={algebra},
  url_Paper={https://www.sciencedirect.com/science/article/pii/S0021869385712070},
  abstract={In recent papers J. Bergen and D.S. Passman have applied so-called
`Delta methods' to enveloping algebras of Lie superalgebras. This paper
generalizes their results to the class of Lie colour algebras. The
methods and results in this paper are very similar to those of Bergen
and Passman, and many of their proofs generalize easily. However, at
some points there are serious difficulties to overcome. The results
obtained show that if $L$ is a Lie colour algebra then the join of all
finite-dimensional ideals of  $L$ controls certain properties of the
universal enveloping algebras  $U(L)$. Specifically, we consider
primeness, semiprimeness, constants, semi-invariants, almost constants,
faithfulness of the adjoint action, the centre, almost centralizers and
the central closure.}
}

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In order to keep using Mendeley with BibBase past April\n        14th, you need to:\n        <ol>\n          <li>renew the authorization for BibBase on Mendeley, and</li>\n          <li>update the BibBase URL\n            in your page the same way you did when you initially set up\n            this page.\n          </li>\n        </ol>\n      </p>\n\n      <p>\n        <a href=\"http://bibbase.org/cgi-bin/mendeley2/get.py\">\n          <i class=\"fa fa-angle-double-right\"></i>\n          Fix it now</a>\n      </p>\n    </div>\n\n  </div>\n\n\n  <div id=\"bibbase_body\">\n    \n  \n  <div class=\"bibbase_group_whole\" id=\"group_1999\">\n    <div class=\"bibbase_group\"\n      onclick=\"toggleGroup('group_1999')\"\n      onkeypress=\"toggleGroup('group_1999')\"\n      tabindex=\"0\">\n      <i class=\"fa fa-angle-down bibbase_group_head_icon\"></i>&nbsp;\n      <span>1999</span>\n      <span class=\"bibbase_group_count\">\n        \n        (4)\n        \n      </span>\n    </div>\n    <div class=\"bibbase_group_body\">\n      \n  \n  <div class=\"bibbase_paper\" id=\"bergen-wilson-xinnerautomorphismsofsemicommutativequantumalgebras-1999\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  Bergen, J.;  and <a class=\"bibbase author link\" href=\"https://markcwilson.site/Research/Outputs/papers.html\">Wilson, M. C.</a>\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  <a href=\"https://www.sciencedirect.com/science/article/pii/S0021869399979279\"\n     onclick=\"return trackOutboundLink('publications', 'click', 'bergen-wilson-xinnerautomorphismsofsemicommutativequantumalgebras-1999', 'https://www.sciencedirect.com/science/article/pii/S0021869399979279', event);\">\n    X-inner automorphisms of semi-commutative quantum algebras.\n  </a>\n  \n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Journal of Algebra</i>, 220(1): 152-173.  1999.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://www.sciencedirect.com/science/article/pii/S0021869399979279\"\n     onclick=\"log_download('bergen-wilson-xinnerautomorphismsofsemicommutativequantumalgebras-1999', 'https://www.sciencedirect.com/science/article/pii/S0021869399979279', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/link.svg\"\n\t     alt=\"X-inner automorphisms of semi-commutative quantum algebras [link]\"\n       title=\" paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\"> paper</span></a>\n  &nbsp;\n  \n\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/bergen-wilson-xinnerautomorphismsofsemicommutativequantumalgebras-1999\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('bergen-wilson-xinnerautomorphismsofsemicommutativequantumalgebras-1999')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@article{bergen1999x,\n  title={X-inner automorphisms of semi-commutative quantum algebras},\n  author={Bergen, Jeffrey and Wilson, Mark C.},\n  journal={Journal of Algebra},\n  volume={220},\n  number={1},\n  pages={152-173},\n  year={1999},\n  publisher={Academic Press},\n  keywords={algebra},\n  url_Paper={https://www.sciencedirect.com/science/article/pii/S0021869399979279},\n  abstract={Many important quantum algebras such as quantum symplectic space,\nquantum euclidean space, quantum matrices, $q$-analogs of the Heisenberg\nalgebra and the quantum Weyl algebra are semi-commutative. In addition,\nenveloping algebras $U(L_+)$ of even Lie color algebras are also\nsemi-commutative. In this paper, we generalize work of Montgomery and\nexamine the X-inner automorphisms of such algebras. The theorems and\nexamples in our paper show that for algebras $R$ of this type, the\nnon-identity X-inner automorphisms of  $R$ tend to have infinite order.\nThus if $G$ is a finite group of automorphisms of $R$, then the action\nof $G$ will be X-outer and this immediately gives useful information\nabout crossed products  $R∗_t G$.}\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  Many important quantum algebras such as quantum symplectic space, quantum euclidean space, quantum matrices, $q$-analogs of the Heisenberg algebra and the quantum Weyl algebra are semi-commutative. In addition, enveloping algebras $U(L_+)$ of even Lie color algebras are also semi-commutative. In this paper, we generalize work of Montgomery and examine the X-inner automorphisms of such algebras. The theorems and examples in our paper show that for algebras $R$ of this type, the non-identity X-inner automorphisms of $R$ tend to have infinite order. Thus if $G$ is a finite group of automorphisms of $R$, then the action of $G$ will be X-outer and this immediately gives useful information about crossed products $R∗_t G$.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"riley-wilson-associativealgebrassatisfyingasemigroupidentity-1999\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  Riley, D.;  and <a class=\"bibbase author link\" href=\"https://markcwilson.site/Research/Outputs/papers.html\">Wilson, M. C.</a>\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  <a href=\"https://www.cambridge.org/core/journals/glasgow-mathematical-journal/article/associative-algebras-satisfying-a-semigroup-identity/89A9FE38678C0635AE59E0B3286291CA\"\n     onclick=\"return trackOutboundLink('publications', 'click', 'riley-wilson-associativealgebrassatisfyingasemigroupidentity-1999', 'https://www.cambridge.org/core/journals/glasgow-mathematical-journal/article/associative-algebras-satisfying-a-semigroup-identity/89A9FE38678C0635AE59E0B3286291CA', event);\">\n    Associative algebras satisfying a semigroup identity.\n  </a>\n  \n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Glasgow Mathematical Journal</i>, 41(3): 453-462.  1999.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://www.cambridge.org/core/journals/glasgow-mathematical-journal/article/associative-algebras-satisfying-a-semigroup-identity/89A9FE38678C0635AE59E0B3286291CA\"\n     onclick=\"log_download('riley-wilson-associativealgebrassatisfyingasemigroupidentity-1999', 'https://www.cambridge.org/core/journals/glasgow-mathematical-journal/article/associative-algebras-satisfying-a-semigroup-identity/89A9FE38678C0635AE59E0B3286291CA', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/link.svg\"\n\t     alt=\"Associative algebras satisfying a semigroup identity [link]\"\n       title=\" paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\"> paper</span></a>\n  &nbsp;\n  \n\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/riley-wilson-associativealgebrassatisfyingasemigroupidentity-1999\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('riley-wilson-associativealgebrassatisfyingasemigroupidentity-1999')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@article{riley1999associative,\n  title={Associative algebras satisfying a semigroup identity},\n  author={Riley, D.M. and Wilson, Mark C.},\n  journal={Glasgow Mathematical Journal},\n  volume={41},\n  number={3},\n  pages={453-462},\n  year={1999},\n  publisher={Cambridge University Press},\n  keywords={algebra},\n  url_Paper={https://www.cambridge.org/core/journals/glasgow-mathematical-journal/article/associative-algebras-satisfying-a-semigroup-identity/89A9FE38678C0635AE59E0B3286291CA},\n  abstract={Denote by $(R,\\cdot)$ the multiplicative semigroup of an associative\nalgebra $R$ over an infinite field, and let $(R,\\circ)$ represent $R$\nwhen viewed as a semigroup via the circle operation $x\\circ y=x+y+xy$.\nIn this paper we characterize the existence of an identity in these\nsemigroups in terms of the Lie structure of $R$. Namely, we prove that\nthe following conditions on $R$ are equivalent: the semigroup\n$(R,\\circ)$ satisfies an identity; the semigroup $(R,\\cdot)$ satisfies a\nreduced identity; and, the associated Lie algebra of $R$ satisfies the\nEngel condition. When $R$ is finitely generated these conditions are\neach equivalent to $R$ being upper Lie nilpotent.}\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  Denote by $(R,·)$ the multiplicative semigroup of an associative algebra $R$ over an infinite field, and let $(R,∘)$ represent $R$ when viewed as a semigroup via the circle operation $x∘ y=x+y+xy$. In this paper we characterize the existence of an identity in these semigroups in terms of the Lie structure of $R$. Namely, we prove that the following conditions on $R$ are equivalent: the semigroup $(R,∘)$ satisfies an identity; the semigroup $(R,·)$ satisfies a reduced identity; and, the associated Lie algebra of $R$ satisfies the Engel condition. When $R$ is finitely generated these conditions are each equivalent to $R$ being upper Lie nilpotent.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"riley-wilson-groupalgebrasandenvelopingalgebraswithnonmatrixandsemigroupidentities-1999\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  Riley, D.;  and <a class=\"bibbase author link\" href=\"https://markcwilson.site/Research/Outputs/papers.html\">Wilson, M. C.</a>\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  <a href=\"https://www.tandfonline.com/doi/abs/10.1080/00927879908826645\"\n     onclick=\"return trackOutboundLink('publications', 'click', 'riley-wilson-groupalgebrasandenvelopingalgebraswithnonmatrixandsemigroupidentities-1999', 'https://www.tandfonline.com/doi/abs/10.1080/00927879908826645', event);\">\n    Group algebras and enveloping algebras with nonmatrix and semigroup identities.\n  </a>\n  \n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Communications in Algebra</i>, 27(7): 3545-3556.  1999.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://www.tandfonline.com/doi/abs/10.1080/00927879908826645\"\n     onclick=\"log_download('riley-wilson-groupalgebrasandenvelopingalgebraswithnonmatrixandsemigroupidentities-1999', 'https://www.tandfonline.com/doi/abs/10.1080/00927879908826645', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/link.svg\"\n\t     alt=\"Group algebras and enveloping algebras with nonmatrix and semigroup identities [link]\"\n       title=\" paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\"> paper</span></a>\n  &nbsp;\n  \n\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/riley-wilson-groupalgebrasandenvelopingalgebraswithnonmatrixandsemigroupidentities-1999\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('riley-wilson-groupalgebrasandenvelopingalgebraswithnonmatrixandsemigroupidentities-1999')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@article{riley1999group,\n  title={Group algebras and enveloping algebras with nonmatrix and semigroup identities},\n  author={Riley, D.M. and Wilson, Mark C.},\n  journal={Communications in Algebra},\n  volume={27},\n  number={7},\n  pages={3545-3556},\n  year={1999},\n  publisher={Taylor \\&amp; Francis},\n  keywords={algebra},\n  url_Paper={https://www.tandfonline.com/doi/abs/10.1080/00927879908826645},\n  abstract={Let $K$ be a field of characteristic $p&gt;0$.  Denote by $\\omega(R)$ the\naugmentation ideal of either a group algebra $R=K[G]$ or a restricted\nenveloping algebra $R=u(L)$ over $K$.   We first characterize those $R$\nfor which $\\omega(R)$ satisfies a polynomial identity not satisfied by\nthe algebra of all $2\\times 2$ matrices over $K$. Then, we examine those\n$R$ for which $\\omega(R)$ satisfies a semigroup identity (that is, a\npolynomial identity which can be written as the difference of two\nmonomials).}\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  Let $K$ be a field of characteristic $p>0$. Denote by $ω(R)$ the augmentation ideal of either a group algebra $R=K[G]$ or a restricted enveloping algebra $R=u(L)$ over $K$. We first characterize those $R$ for which $ω(R)$ satisfies a polynomial identity not satisfied by the algebra of all $2× 2$ matrices over $K$. Then, we examine those $R$ for which $ω(R)$ satisfies a semigroup identity (that is, a polynomial identity which can be written as the difference of two monomials).\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"riley-wilson-associativeringssatisfyingtheengelcondition-1999\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  Riley, D.;  and <a class=\"bibbase author link\" href=\"https://markcwilson.site/Research/Outputs/papers.html\">Wilson, M. C.</a>\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  <a href=\"https://www.ams.org/journals/proc/1999-127-04/S0002-9939-99-04643-2/S0002-9939-99-04643-2.pdf\"\n     onclick=\"return trackOutboundLink('publications', 'click', 'riley-wilson-associativeringssatisfyingtheengelcondition-1999', 'https://www.ams.org/journals/proc/1999-127-04/S0002-9939-99-04643-2/S0002-9939-99-04643-2.pdf', event);\">\n    Associative rings satisfying the Engel condition.\n  </a>\n  \n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Proceedings of the American Mathematical Society</i>, 127(4): 973-976.  1999.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://www.ams.org/journals/proc/1999-127-04/S0002-9939-99-04643-2/S0002-9939-99-04643-2.pdf\"\n     onclick=\"log_download('riley-wilson-associativeringssatisfyingtheengelcondition-1999', 'https://www.ams.org/journals/proc/1999-127-04/S0002-9939-99-04643-2/S0002-9939-99-04643-2.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"Associative rings satisfying the Engel condition [pdf]\"\n       title=\" paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\"> paper</span></a>\n  &nbsp;\n  \n\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/riley-wilson-associativeringssatisfyingtheengelcondition-1999\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('riley-wilson-associativeringssatisfyingtheengelcondition-1999')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@article{riley1999associative,\n  title={Associative rings satisfying the Engel condition},\n  author={Riley, D.M. and Wilson, Mark C.},\n  journal={Proceedings of the American Mathematical Society},\n  volume={127},\n  number={4},\n  pages={973-976},\n  year={1999},\n  keywords={algebra},\n  url_Paper={https://www.ams.org/journals/proc/1999-127-04/S0002-9939-99-04643-2/S0002-9939-99-04643-2.pdf},\n  abstract={Let $C$ be a commutative ring, and let $R$ be an associative $C$-algebra\ngenerated by elements $\\{x_1,\\ldots,x_d\\}$. We show that if $R$\nsatisfies the Engel condition of degree $n$ then $R$ is upper Lie\nnilpotent of class bounded by a function that depends only on $d$ and\n$n$. We deduce that the Engel condition in an arbitrary associative ring\nis inherited by its group of units, and implies a semigroup identity.}\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  Let $C$ be a commutative ring, and let $R$ be an associative $C$-algebra generated by elements $\\{x_1,…,x_d\\}$. We show that if $R$ satisfies the Engel condition of degree $n$ then $R$ is upper Lie nilpotent of class bounded by a function that depends only on $d$ and $n$. We deduce that the Engel condition in an arbitrary associative ring is inherited by its group of units, and implies a semigroup identity.\n</div>\n\n\n</div>\n\n\n\n\n\n    </div>\n  </div>\n\n  <div class=\"bibbase_group_whole\" id=\"group_1998\">\n    <div class=\"bibbase_group\"\n      onclick=\"toggleGroup('group_1998')\"\n      onkeypress=\"toggleGroup('group_1998')\"\n      tabindex=\"0\">\n      <i class=\"fa fa-angle-down bibbase_group_head_icon\"></i>&nbsp;\n      <span>1998</span>\n      <span class=\"bibbase_group_count\">\n        \n        (3)\n        \n      </span>\n    </div>\n    <div class=\"bibbase_group_body\">\n      \n  \n  <div class=\"bibbase_paper\" id=\"wilson-primitiveidealsinhopfalgebraextensions-1998\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  <a class=\"bibbase author link\" href=\"https://markcwilson.site/Research/Outputs/papers.html\">Wilson, M. C.</a>\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  <a href=\"https://arxiv.org/pdf/math/9808122.pdf\"\n     onclick=\"return trackOutboundLink('publications', 'click', 'wilson-primitiveidealsinhopfalgebraextensions-1998', 'https://arxiv.org/pdf/math/9808122.pdf', event);\">\n    Primitive ideals in Hopf algebra extensions.\n  </a>\n  \n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>arXiv preprint math/9808122</i>.  1998.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://arxiv.org/pdf/math/9808122.pdf\"\n     onclick=\"log_download('wilson-primitiveidealsinhopfalgebraextensions-1998', 'https://arxiv.org/pdf/math/9808122.pdf', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/pdf.svg\"\n\t     alt=\"Primitive ideals in Hopf algebra extensions [pdf]\"\n       title=\" paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\"> paper</span></a>\n  &nbsp;\n  \n\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/wilson-primitiveidealsinhopfalgebraextensions-1998\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('wilson-primitiveidealsinhopfalgebraextensions-1998')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@article{wilson1998primitive,\n  title={Primitive ideals in Hopf algebra extensions},\n  author={Wilson, Mark C.},\n  journal={arXiv preprint math/9808122},\n  year={1998},\n  keywords={algebra},\n  url_Paper={https://arxiv.org/pdf/math/9808122.pdf},\n  abstract={My last paper in algebra, never published formally.}\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  My last paper in algebra, never published formally.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"wilson-bellsprimenesscriterionandthesimpleliesuperalgebras-1998\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  <a class=\"bibbase author link\" href=\"https://markcwilson.site/Research/Outputs/papers.html\">Wilson, M. C.</a>\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  <a href=\"https://www.sciencedirect.com/science/article/pii/S0022404997001990\"\n     onclick=\"return trackOutboundLink('publications', 'click', 'wilson-bellsprimenesscriterionandthesimpleliesuperalgebras-1998', 'https://www.sciencedirect.com/science/article/pii/S0022404997001990', event);\">\n    Bell's primeness criterion and the simple Lie superalgebras.\n  </a>\n  \n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Journal of Pure and Applied Algebra</i>, 133(1-2): 241-260.  1998.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://www.sciencedirect.com/science/article/pii/S0022404997001990\"\n     onclick=\"log_download('wilson-bellsprimenesscriterionandthesimpleliesuperalgebras-1998', 'https://www.sciencedirect.com/science/article/pii/S0022404997001990', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/link.svg\"\n\t     alt=\"Bell&#x27;s primeness criterion and the simple Lie superalgebras [link]\"\n       title=\" paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\"> paper</span></a>\n  &nbsp;\n  \n\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/wilson-bellsprimenesscriterionandthesimpleliesuperalgebras-1998\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('wilson-bellsprimenesscriterionandthesimpleliesuperalgebras-1998')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@article{wilson1998bell,\n  title={Bell&#x27;s primeness criterion and the simple Lie superalgebras},\n  author={Wilson, Mark C.},\n  journal={Journal of Pure and Applied Algebra},\n  volume={133},\n  number={1-2},\n  pages={241-260},\n  year={1998},\n  publisher={North-Holland},\n  keywords={algebra},\n  url_Paper={https://www.sciencedirect.com/science/article/pii/S0022404997001990},\n  abstract={We determine all finite-dimensional simple Lie superalgebras $L$ such\nthat $U(L)$ satisfies a primeness criterion due to Bell. Some open\nproblems related to primeness of enveloping algebras are listed.}\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  We determine all finite-dimensional simple Lie superalgebras $L$ such that $U(L)$ satisfies a primeness criterion due to Bell. Some open problems related to primeness of enveloping algebras are listed.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"wilson-pritchard-primenessoftheenvelopingalgebraofthespecialliesuperalgebras-1998\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  <a class=\"bibbase author link\" href=\"https://markcwilson.site/Research/Outputs/papers.html\">Wilson, M. C.</a>;  and Pritchard, G.\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  <a href=\"https://link.springer.com/article/10.1007/s000130050183\"\n     onclick=\"return trackOutboundLink('publications', 'click', 'wilson-pritchard-primenessoftheenvelopingalgebraofthespecialliesuperalgebras-1998', 'https://link.springer.com/article/10.1007/s000130050183', event);\">\n    Primeness of the enveloping algebra of the special Lie superalgebras.\n  </a>\n  \n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Archiv der Mathematik</i>, 70(3): 187-196.  1998.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://link.springer.com/article/10.1007/s000130050183\"\n     onclick=\"log_download('wilson-pritchard-primenessoftheenvelopingalgebraofthespecialliesuperalgebras-1998', 'https://link.springer.com/article/10.1007/s000130050183', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/link.svg\"\n\t     alt=\"Primeness of the enveloping algebra of the special Lie superalgebras [link]\"\n       title=\" paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\"> paper</span></a>\n  &nbsp;\n  \n\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/wilson-pritchard-primenessoftheenvelopingalgebraofthespecialliesuperalgebras-1998\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('wilson-pritchard-primenessoftheenvelopingalgebraofthespecialliesuperalgebras-1998')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@article{wilson1998primeness,\n  title={Primeness of the enveloping algebra of the special Lie superalgebras},\n  author={Wilson, Mark C. and Pritchard, Geoffrey},\n  journal={Archiv der Mathematik},\n  volume={70},\n  number={3},\n  pages={187-196},\n  year={1998},\n  publisher={Birkh{\\&quot;a}user Verlag},\n  keywords={algebra},\n  url_Paper={https://link.springer.com/article/10.1007/s000130050183},\n  abstract={A primeness criterion due to Bell is shown to apply to the universal\nenveloping algebra of the Cartan type Lie superalgebras $S(V)$ and\n$\\widetilde{S}(V;t)$ when $\\dim V$ is even. On the other hand, if $\\dim\nV$ is odd then $U(S(V))$ is never semiprime.}\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  A primeness criterion due to Bell is shown to apply to the universal enveloping algebra of the Cartan type Lie superalgebras $S(V)$ and $\\widetilde{S}(V;t)$ when $\\dim V$ is even. On the other hand, if $\\dim V$ is odd then $U(S(V))$ is never semiprime.\n</div>\n\n\n</div>\n\n\n\n\n\n    </div>\n  </div>\n\n  <div class=\"bibbase_group_whole\" id=\"group_1997\">\n    <div class=\"bibbase_group\"\n      onclick=\"toggleGroup('group_1997')\"\n      onkeypress=\"toggleGroup('group_1997')\"\n      tabindex=\"0\">\n      <i class=\"fa fa-angle-down bibbase_group_head_icon\"></i>&nbsp;\n      <span>1997</span>\n      <span class=\"bibbase_group_count\">\n        \n        (3)\n        \n      </span>\n    </div>\n    <div class=\"bibbase_group_body\">\n      \n  \n  <div class=\"bibbase_paper\" id=\"wilson-crossedproductsofrestrictedenvelopingalgebras-1997\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  <a class=\"bibbase author link\" href=\"https://markcwilson.site/Research/Outputs/papers.html\">Wilson, M. C.</a>\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  <a href=\"https://www.tandfonline.com/doi/abs/10.1080/00927879708825868\"\n     onclick=\"return trackOutboundLink('publications', 'click', 'wilson-crossedproductsofrestrictedenvelopingalgebras-1997', 'https://www.tandfonline.com/doi/abs/10.1080/00927879708825868', event);\">\n    Crossed products of restricted enveloping algebras.\n  </a>\n  \n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Communications in Algebra</i>, 25(2): 487-496.  1997.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://www.tandfonline.com/doi/abs/10.1080/00927879708825868\"\n     onclick=\"log_download('wilson-crossedproductsofrestrictedenvelopingalgebras-1997', 'https://www.tandfonline.com/doi/abs/10.1080/00927879708825868', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/link.svg\"\n\t     alt=\"Crossed products of restricted enveloping algebras [link]\"\n       title=\" paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\"> paper</span></a>\n  &nbsp;\n  \n\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/wilson-crossedproductsofrestrictedenvelopingalgebras-1997\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('wilson-crossedproductsofrestrictedenvelopingalgebras-1997')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@article{wilson1997crossed,\n  title={Crossed products of restricted enveloping algebras},\n  author={Wilson, Mark C.},\n  journal={Communications in Algebra},\n  volume={25},\n  number={2},\n  pages={487-496},\n  year={1997},\n  publisher={Taylor \\&amp; Francis},\n  keywords={algebra},\n  url_Paper={https://www.tandfonline.com/doi/abs/10.1080/00927879708825868},\n  abstract={Let $K$ be a field of characteristic $p&gt;0$, let $L$ be a restricted Lie\nalgebra and let $R$ be an associative $K$-algebra. It is shown that the\nvarious constructions in the literature of crossed product of  $R$ with\n$u(L)$ are equivalent. We calculate explicit formulae relating the\nparameters involved and obtain a formula which hints at a noncommutative\nversion of the Bell polynomials.}\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  Let $K$ be a field of characteristic $p>0$, let $L$ be a restricted Lie algebra and let $R$ be an associative $K$-algebra. It is shown that the various constructions in the literature of crossed product of $R$ with $u(L)$ are equivalent. We calculate explicit formulae relating the parameters involved and obtain a formula which hints at a noncommutative version of the Bell polynomials.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"wilson-pritchard-wood-bellsprimenesscriterionforw2n1-1997\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  <a class=\"bibbase author link\" href=\"https://markcwilson.site/Research/Outputs/papers.html\">Wilson, M. C.</a>; Pritchard, G.;  and Wood, D. H.\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  <a href=\"https://doi.org/10.1080/10586458.1997.10504352\"\n     onclick=\"return trackOutboundLink('publications', 'click', 'wilson-pritchard-wood-bellsprimenesscriterionforw2n1-1997', 'https://doi.org/10.1080/10586458.1997.10504352', event);\">\n    Bell's primeness criterion for $W(2n+ 1)$.\n  </a>\n  \n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Experimental Mathematics</i>, 6(1): 77-85.  1997.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://doi.org/10.1080/10586458.1997.10504352\"\n     onclick=\"log_download('wilson-pritchard-wood-bellsprimenesscriterionforw2n1-1997', 'https://doi.org/10.1080/10586458.1997.10504352', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/link.svg\"\n\t     alt=\"Bell&#x27;s primeness criterion for $W(2n+ 1)$ [link]\"\n       title=\" paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\"> paper</span></a>\n  &nbsp;\n  \n\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/wilson-pritchard-wood-bellsprimenesscriterionforw2n1-1997\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('wilson-pritchard-wood-bellsprimenesscriterionforw2n1-1997')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@article{wilson1997bell,\n  title={Bell&#x27;s primeness criterion for $W(2n+ 1)$},\n  author={Wilson, Mark C. and Pritchard, Geoffrey and Wood, David H.},\n  journal={Experimental Mathematics},\n  volume={6},\n  number={1},\n  pages={77-85},\n  year={1997},\n  publisher={Taylor \\&amp; Francis Group},\n  keywords={algebra},\n  url_Paper={https://doi.org/10.1080/10586458.1997.10504352},\n  abstract={On the basis of experimental work involving matrix computations, we\nconjecture that a criterion due to Bell for primeness of the universal\nenveloping algebra of a Lie superalgebra applies to the Cartan type Lie\nsuperalgebras $W(n)$ for $n=3$ but does not apply for odd $n\\geq 5$. The\nexperiments lead to a rigorous proof, which we present.}\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  On the basis of experimental work involving matrix computations, we conjecture that a criterion due to Bell for primeness of the universal enveloping algebra of a Lie superalgebra applies to the Cartan type Lie superalgebras $W(n)$ for $n=3$ but does not apply for odd $n≥ 5$. The experiments lead to a rigorous proof, which we present.\n</div>\n\n\n</div>\n\n\n  <div class=\"bibbase_paper\" id=\"wilson-primenessoftheenvelopingalgebraofhamiltoniansuperalgebras-1997\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  <a class=\"bibbase author link\" href=\"https://markcwilson.site/Research/Outputs/papers.html\">Wilson, M. C.</a>\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  <a href=\"https://www.cambridge.org/core/journals/bulletin-of-the-australian-mathematical-society/article/primeness-of-the-enveloping-algebra-of-hamiltonian-superalgebras/A643AA62E4FAC8098924C1DE44E463C8\"\n     onclick=\"return trackOutboundLink('publications', 'click', 'wilson-primenessoftheenvelopingalgebraofhamiltoniansuperalgebras-1997', 'https://www.cambridge.org/core/journals/bulletin-of-the-australian-mathematical-society/article/primeness-of-the-enveloping-algebra-of-hamiltonian-superalgebras/A643AA62E4FAC8098924C1DE44E463C8', event);\">\n    Primeness of the enveloping algebra of Hamiltonian superalgebras.\n  </a>\n  \n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Bulletin of the Australian Mathematical Society</i>, 56(3): 483-488.  1997.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://www.cambridge.org/core/journals/bulletin-of-the-australian-mathematical-society/article/primeness-of-the-enveloping-algebra-of-hamiltonian-superalgebras/A643AA62E4FAC8098924C1DE44E463C8\"\n     onclick=\"log_download('wilson-primenessoftheenvelopingalgebraofhamiltoniansuperalgebras-1997', 'https://www.cambridge.org/core/journals/bulletin-of-the-australian-mathematical-society/article/primeness-of-the-enveloping-algebra-of-hamiltonian-superalgebras/A643AA62E4FAC8098924C1DE44E463C8', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/link.svg\"\n\t     alt=\"Primeness of the enveloping algebra of Hamiltonian superalgebras [link]\"\n       title=\" paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\"> paper</span></a>\n  &nbsp;\n  \n\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/wilson-primenessoftheenvelopingalgebraofhamiltoniansuperalgebras-1997\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('wilson-primenessoftheenvelopingalgebraofhamiltoniansuperalgebras-1997')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@article{wilson1997primeness,\n  title={Primeness of the enveloping algebra of Hamiltonian superalgebras},\n  author={Wilson, Mark C.},\n  journal={Bulletin of the Australian Mathematical Society},\n  volume={56},\n  number={3},\n  pages={483-488},\n  year={1997},\n  publisher={Cambridge University Press},\n  keywords={algebra},\n  url_Paper={https://www.cambridge.org/core/journals/bulletin-of-the-australian-mathematical-society/article/primeness-of-the-enveloping-algebra-of-hamiltonian-superalgebras/A643AA62E4FAC8098924C1DE44E463C8},\n  abstract={In 1990 Allen Bell presented a sufficient condition for the primeness of\nthe universal enveloping algebra of a Lie superalgebra. Let $Q$ be a\nnonsingular bilinear form on a finite-dimensional vector space over a\nfield of characteristic zero. In this paper we show that Bell&#x27;s\ncriterion applies to the Hamiltonian Cartan type superalgebras\ndetermined by $Q$, and hence obtain some new prime noetherian rings.}\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  In 1990 Allen Bell presented a sufficient condition for the primeness of the universal enveloping algebra of a Lie superalgebra. Let $Q$ be a nonsingular bilinear form on a finite-dimensional vector space over a field of characteristic zero. In this paper we show that Bell's criterion applies to the Hamiltonian Cartan type superalgebras determined by $Q$, and hence obtain some new prime noetherian rings.\n</div>\n\n\n</div>\n\n\n\n\n\n    </div>\n  </div>\n\n  <div class=\"bibbase_group_whole\" id=\"group_1996\">\n    <div class=\"bibbase_group\"\n      onclick=\"toggleGroup('group_1996')\"\n      onkeypress=\"toggleGroup('group_1996')\"\n      tabindex=\"0\">\n      <i class=\"fa fa-angle-down bibbase_group_head_icon\"></i>&nbsp;\n      <span>1996</span>\n      <span class=\"bibbase_group_count\">\n        \n        (1)\n        \n      </span>\n    </div>\n    <div class=\"bibbase_group_body\">\n      \n  \n  <div class=\"bibbase_paper\" id=\"wilson-primenessoftheenvelopingalgebraofacartantypeliesuperalgebra-1996\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  <a class=\"bibbase author link\" href=\"https://markcwilson.site/Research/Outputs/papers.html\">Wilson, M. C.</a>\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  <a href=\"https://drive.google.com/uc?export=download&amp;id=1NEXsxwRAx2CWt43v0y0jyZdP1LdOS_xF\"\n     onclick=\"return trackOutboundLink('publications', 'click', 'wilson-primenessoftheenvelopingalgebraofacartantypeliesuperalgebra-1996', 'https://drive.google.com/uc?export=download&amp;id=1NEXsxwRAx2CWt43v0y0jyZdP1LdOS_xF', event);\">\n    Primeness of the enveloping algebra of a Cartan type Lie superalgebra.\n  </a>\n  \n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Proceedings of the American Mathematical Society</i>, 124(2): 383-387.  1996.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://drive.google.com/uc?export=download&amp;id=1NEXsxwRAx2CWt43v0y0jyZdP1LdOS_xF\"\n     onclick=\"log_download('wilson-primenessoftheenvelopingalgebraofacartantypeliesuperalgebra-1996', 'https://drive.google.com/uc?export=download&amp;id=1NEXsxwRAx2CWt43v0y0jyZdP1LdOS_xF', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/link.svg\"\n\t     alt=\"Primeness of the enveloping algebra of a Cartan type Lie superalgebra [link]\"\n       title=\" paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\"> paper</span></a>\n  &nbsp;\n  \n\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/wilson-primenessoftheenvelopingalgebraofacartantypeliesuperalgebra-1996\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('wilson-primenessoftheenvelopingalgebraofacartantypeliesuperalgebra-1996')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@article{wilson1996primeness,\n  title={Primeness of the enveloping algebra of a Cartan type Lie superalgebra},\n  author={Wilson, Mark C.},\n  journal={Proceedings of the American Mathematical Society},\n  volume={124},\n  number={2},\n  pages={383-387},\n  year={1996},\n  keywords={algebra},\n  url_Paper={},\n  abstract={We show that a primeness criterion for enveloping algebras of Lie\nsuperalgebras discovered by Bell is applicable to the Cartan type Lie\nsuperalgebras $W(n)$, $n$ even. Other algebras are considered but there\nare no definitive answers in these cases.}\n}\n\n\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  We show that a primeness criterion for enveloping algebras of Lie superalgebras discovered by Bell is applicable to the Cartan type Lie superalgebras $W(n)$, $n$ even. Other algebras are considered but there are no definitive answers in these cases.\n</div>\n\n\n</div>\n\n\n\n\n\n    </div>\n  </div>\n\n  <div class=\"bibbase_group_whole\" id=\"group_1995\">\n    <div class=\"bibbase_group\"\n      onclick=\"toggleGroup('group_1995')\"\n      onkeypress=\"toggleGroup('group_1995')\"\n      tabindex=\"0\">\n      <i class=\"fa fa-angle-down bibbase_group_head_icon\"></i>&nbsp;\n      <span>1995</span>\n      <span class=\"bibbase_group_count\">\n        \n        (1)\n        \n      </span>\n    </div>\n    <div class=\"bibbase_group_body\">\n      \n  \n  <div class=\"bibbase_paper\" id=\"wilson-deltamethodsinenvelopingalgebrasofliecoloralgebras-1995\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_author\">\n  <a class=\"bibbase author link\" href=\"https://markcwilson.site/Research/Outputs/papers.html\">Wilson, M. C.</a>\n</span>\n\n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  <a href=\"https://www.sciencedirect.com/science/article/pii/S0021869385712070\"\n     onclick=\"return trackOutboundLink('publications', 'click', 'wilson-deltamethodsinenvelopingalgebrasofliecoloralgebras-1995', 'https://www.sciencedirect.com/science/article/pii/S0021869385712070', event);\">\n    Delta methods in enveloping algebras of Lie color algebras.\n  </a>\n  \n  \n  \n</span>\n\n  \n\n</span>\n\n  <i>Journal of Algebra</i>, 175(2): 661-696.  1995.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://www.sciencedirect.com/science/article/pii/S0021869385712070\"\n     onclick=\"log_download('wilson-deltamethodsinenvelopingalgebrasofliecoloralgebras-1995', 'https://www.sciencedirect.com/science/article/pii/S0021869385712070', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/link.svg\"\n\t     alt=\"Delta methods in enveloping algebras of Lie color algebras [link]\"\n       title=\" paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\"> paper</span></a>\n  &nbsp;\n  \n\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/wilson-deltamethodsinenvelopingalgebrasofliecoloralgebras-1995\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('wilson-deltamethodsinenvelopingalgebrasofliecoloralgebras-1995')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@article{wilson1995delta,\n  title={Delta methods in enveloping algebras of Lie color algebras},\n  author={Wilson, Mark C.},\n  journal={Journal of Algebra},\n  volume={175},\n  number={2},\n  pages={661-696},\n  year={1995},\n  publisher={Academic Press},\n  keywords={algebra},\n  url_Paper={https://www.sciencedirect.com/science/article/pii/S0021869385712070},\n  abstract={In recent papers J. Bergen and D.S. Passman have applied so-called\n&#x60;Delta methods&#x27; to enveloping algebras of Lie superalgebras. This paper\ngeneralizes their results to the class of Lie colour algebras. The\nmethods and results in this paper are very similar to those of Bergen\nand Passman, and many of their proofs generalize easily. However, at\nsome points there are serious difficulties to overcome. The results\nobtained show that if $L$ is a Lie colour algebra then the join of all\nfinite-dimensional ideals of  $L$ controls certain properties of the\nuniversal enveloping algebras  $U(L)$. Specifically, we consider\nprimeness, semiprimeness, constants, semi-invariants, almost constants,\nfaithfulness of the adjoint action, the centre, almost centralizers and\nthe central closure.}\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  In recent papers J. Bergen and D.S. Passman have applied so-called `Delta methods' to enveloping algebras of Lie superalgebras. This paper generalizes their results to the class of Lie colour algebras. The methods and results in this paper are very similar to those of Bergen and Passman, and many of their proofs generalize easily. However, at some points there are serious difficulties to overcome. The results obtained show that if $L$ is a Lie colour algebra then the join of all finite-dimensional ideals of $L$ controls certain properties of the universal enveloping algebras $U(L)$. Specifically, we consider primeness, semiprimeness, constants, semi-invariants, almost constants, faithfulness of the adjoint action, the centre, almost centralizers and the central closure.\n</div>\n\n\n</div>\n\n\n\n\n\n    </div>\n  </div>\n\n\n\n\n  </div>\n\n\n  <!-- Modal -->\n\n  <!-- <iframe id=\"bibbase_network_frame\" -->\n  <!--         src=\"//bibbase.org/network/control\" -->\n  <!--         style=\"display: none;\"> -->\n  <!-- </iframe> -->\n\n</div>\n"}; document.write(bibbase_data.data);