Classification of finite simple amenable ${\cal Z}$-stable $C^*$-algebras

Guihua Gong; Huaxin Lin; Zhuang Niu

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arXiv · 1501.00135

Classification of finite simple amenable ${\cal Z}$-stable $C^*$-algebras

Guihua Gong·Huaxin Lin·Zhuang Niu

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Abstract

We present a classification theorem for a class of unital simple separable amenable ${\cal Z}$-stable $C^*$-algebras by the Elliott invariant. This class of simple $C^*$-algebras exhausts all possible Elliott invariant for unital stably finite simple separable amenable ${\cal Z}$-stable $C^*$-algebras. Moreover, it contains all unital simple separable amenable $C^*$-alegbras which satisfy the UCT and have finite rational tracial rank.

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Guihua Gong, Huaxin Lin, Zhuang Niu. 2015-11-16. Classification of finite simple amenable ${\cal Z}$-stable $C^*$-algebras. https://arxiv.org/abs/1501.00135

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