On the classification of simple amenable $\mathrm{C}^{}$-algebras with finite decomposition rank, II

We prove that every unital simple separable \mathrm{C}^{*} -algebra A with finite decomposition rank which satisfies the UCT has the property that A\otimes Q has generalized tracial rank at most one, where Q is the universal UHF-algebra. Consequently, A is classifiable in the sense of Elliott.

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Bibliographic Details
Published in:Journal of noncommutative geometry Vol. 19; no. 1; pp. 73 - 104
Main Authors: Elliott, George A., Gong, Guihua, Lin, Huaxin, Niu, Zhuang
Format: Journal Article
Language:English
Published: 14.06.2024
ISSN:1661-6952, 1661-6960
Online Access:Get full text
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Summary:We prove that every unital simple separable \mathrm{C}^{*} -algebra A with finite decomposition rank which satisfies the UCT has the property that A\otimes Q has generalized tracial rank at most one, where Q is the universal UHF-algebra. Consequently, A is classifiable in the sense of Elliott.
ISSN:1661-6952
1661-6960
DOI:10.4171/jncg/560