1501.00135Dec 31, 2014272 pages. This revision has 283 pages

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

Guihua Gong, Huaxin Lin, Zhuang Niu

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 ${\cal Z}$

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-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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