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

JournalsjncgVol. 19, No. 1pp. 73–104

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

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

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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.

Cite this article

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. 19 (2025), no. 1, pp. 73–104

DOI 10.4171/JNCG/560