The classification of simple separable unital locally ASH algebras

George A. Elliott; Guihua Gong; Huaxin Lin; Zhuang Niu

The classification of simple separable unital locally ASH algebras

Operator Algebras 2015-07-16 v2

Authors: George A. Elliott , Guihua Gong , Huaxin Lin , Zhuang Niu

Abstract

Let $A$ be a simple separable unital locally approximately subhomogeneous C*-algebra (locally ASH algebra). It is shown that $A\otimes Q$ can be tracially approximated by unital Elliott-Thomsen algebras with trivial $\textrm{K}_1$ -group, where $Q$ is the universal UHF algebra. In particular, it follows that $A$ is classifiable by the Elliott invariant if $A$ is Jiang-Su stable.

Keywords

locally ASH algebras C*-algebras tracial approximation Elliott classification K-theory Jiang-Su stability operator algebras

Cite

@article{arxiv.1506.02308,
  title  = {The classification of simple separable unital locally ASH algebras},
  author = {George A. Elliott and Guihua Gong and Huaxin Lin and Zhuang Niu},
  journal= {arXiv preprint arXiv:1506.02308},
  year   = {2015}
}

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40 pages

The classification of simple separable unital locally ASH algebras

Abstract

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