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

Guihua Gong; Huaxin Lin; Zhuang Niu

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

Operator Algebras 2015-11-17 v6

Authors: 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 ${\cal Z}$ -stable $C^*$ -algebras. Moreover, it contains all unital simple separable amenable $C^*$ -alegbras which satisfy the UCT and have finite rational tracial rank.

Keywords

C*-algebras Elliott invariant amenable Z-stable classification UCT tracial rank

Cite

@article{arxiv.1501.00135,
  title  = {Classification of finite simple amenable ${\cal Z}$-stable $C^*$-algebras},
  author = {Guihua Gong and Huaxin Lin and Zhuang Niu},
  journal= {arXiv preprint arXiv:1501.00135},
  year   = {2015}
}

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272 pages. This revision has 283 pages

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

Abstract

Keywords

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