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arXiv · 1507.03437

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

George A. Elliott·Guihua Gong·Huaxin Lin·Zhuang Niu
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Abstract

We prove that every unital stably finite simple amenable $C^*$-algebra $A$ with finite nuclear dimension and with UCT such that every trace is quasi-diagonal 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. 2015-07-13. On the classification of simple amenable $C*$-algebras with finite decomposition rank, II. https://arxiv.org/abs/1507.03437

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