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

George A. Elliott; Zhuang Niu

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

Operator Algebras 2016-02-03 v2

Authors: George A. Elliott , Zhuang Niu

Abstract

Let $A$ be a unital simple separable C*-algebra satisfying the UCT. Assume that $\mathrm{dr}(A)<+\infty$ , $A$ is Jiang-Su stable, and $\mathrm{K}_0(A)\otimes \mathbb{Q}\cong \mathbb{Q}$ . Then $A$ is an ASH algebra (indeed, $A$ is a rationally AH algebra).

Keywords

simple C*-algebra amenable C*-algebra finite decomposition rank UCT Jiang-Su stability ASH algebra classification

Cite

@article{arxiv.1507.07876,
  title  = {On the classification of simple amenable C*-algebras with finite decomposition rank},
  author = {George A. Elliott and Zhuang Niu},
  journal= {arXiv preprint arXiv:1507.07876},
  year   = {2016}
}

Comments

10 pages; Part I of arXiv:1507.03437; To appear in "Operator Algebras and their Applications: A Tribute to Richard V. Kadison", Contemporary Mathematics, Amer. Math. Soc., Providence, R. I., 2016

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

Abstract

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