A vector space basis of the quantum symplectic sphere

A vector space basis of the quantum symplectic sphere. Mikkelsen, S. E. arXiv:2107.01406 [math], July, 2021. arXiv: 2107.01406 version: 1

Paper abstract bibtex

We give a candidate of a vector space basis for the algebra ${\}mathcal\{O\}(S_q{\textasciicircum}\{4n-1\})$ of the quantum symplectic sphere for every $n{\}geq 1$. The construction follows by a non-trivial application of the Diamond Lemma. The conjecture is supported by computer experiments for $n=1,2,...,8$. The work is motivated by a result of Landi and D'Andrea, who proved that the first $n-1$ generators of the $C{\textasciicircum}*$-algebra $C(S_q{\textasciicircum}\{(4n-1)\}), n{\}geq 2$ are zero. By finding a vector space basis, we can conclude that these generators are different from zero in the corresponding algebra ${\}mathcal\{O\}(S_q{\textasciicircum}\{4n-1\})$.

@article{mikkelsen_vector_2021,
	title = {A vector space basis of the quantum symplectic sphere},
	url = {http://arxiv.org/abs/2107.01406},
	abstract = {We give a candidate of a vector space basis for the algebra \${\textbackslash}mathcal\{O\}(S\_q{\textasciicircum}\{4n-1\})\$ of the quantum symplectic sphere for every \$n{\textbackslash}geq 1\$. The construction follows by a non-trivial application of the Diamond Lemma. The conjecture is supported by computer experiments for \$n=1,2,...,8\$. The work is motivated by a result of Landi and D'Andrea, who proved that the first \$n-1\$ generators of the \$C{\textasciicircum}*\$-algebra \$C(S\_q{\textasciicircum}\{(4n-1)\}), n{\textbackslash}geq 2\$ are zero. By finding a vector space basis, we can conclude that these generators are different from zero in the corresponding algebra \${\textbackslash}mathcal\{O\}(S\_q{\textasciicircum}\{4n-1\})\$.},
	urldate = {2021-07-08},
	journal = {arXiv:2107.01406 [math]},
	author = {Mikkelsen, Sophie Emma},
	month = jul,
	year = {2021},
	note = {arXiv: 2107.01406
version: 1},
	keywords = {mentions sympy, quantum algebra, quantum mechanics},
}

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