Decomposition rank of UHF-absorbing C*-algebras

Decomposition rank of UHF-absorbing C*-algebras. Matui, H. & Sato, Y. Duke Mathematical Journal, 163(14):2687–2708, November, 2014. arXiv: 1303.4371

Paper doi abstract bibtex

Let A be a unital separable simple C∗-algebra with a unique tracial state. We prove that if A is nuclear and quasidiagonal, then A tensored with the universal UHFalgebra has decomposition rank at most one. Then it is proved that A is nuclear, quasidiagonal and has strict comparison if and only if A has ﬁnite decomposition rank. For such A, we also give a direct proof that A tensored with a UHF-algebra has tracial rank zero. Applying this characterization, we obtain a counter-example to the Powers-Sakai conjecture.

@article{matui_decomposition_2014,
	title = {Decomposition rank of {UHF}-absorbing {C}*-algebras},
	volume = {163},
	issn = {0012-7094},
	url = {http://arxiv.org/abs/1303.4371},
	doi = {10.1215/00127094-2826908},
	abstract = {Let A be a unital separable simple C∗-algebra with a unique tracial state. We prove that if A is nuclear and quasidiagonal, then A tensored with the universal UHFalgebra has decomposition rank at most one. Then it is proved that A is nuclear, quasidiagonal and has strict comparison if and only if A has ﬁnite decomposition rank. For such A, we also give a direct proof that A tensored with a UHF-algebra has tracial rank zero. Applying this characterization, we obtain a counter-example to the Powers-Sakai conjecture.},
	language = {en},
	number = {14},
	urldate = {2020-12-14},
	journal = {Duke Mathematical Journal},
	author = {Matui, Hiroki and Sato, Yasuhiko},
	month = nov,
	year = {2014},
	note = {arXiv: 1303.4371},
	keywords = {46L06, 46L35, 46L55, Mathematics - Operator Algebras},
	pages = {2687--2708},
}

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