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

George A. Elliott; Guihua Gong; Huaxin Lin; Zhuang Niu

doi:10.4171/jncg/560

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

George A. Elliott
University of Toronto, Toronto, Canada
Guihua Gong
University of Puerto Rico, San Juan, USA
Huaxin Lin
East China Normal University, Shanghai, China; University of Oregon, Eugene, USA; Shanghai Institute of Mathematics and Interdisciplinary Sciences, Shanghai, China
Zhuang Niu
University of Wyoming, Laramie, USA

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

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Abstract

We prove that every unital simple separable $C^{*}$ -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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George A. Elliott, Guihua Gong, Huaxin Lin, Zhuang Niu, On the classification of simple amenable $C^{*}$ -algebras with finite decomposition rank, II. J. Noncommut. Geom. (2024), published online first

DOI 10.4171/JNCG/560