A short return to simple AH-algebras with real rank zero

Huaxin Lin

A short return to simple AH-algebras with real rank zero

Operator Algebras 2011-09-13 v1

Authors: Huaxin Lin

Abstract

Let $A$ be a unital simple AH-algebra with stable rank one and real rank zero such that $kx=0$ for all $x\in {\rm ker}\rho_A,$ the subgroup of infinitesmal elements in $K_0(A),$ and for the same integer $k\ge 1.$ We show that $A$ has tracial rank zero and is isomorphic to a unital simple AH-algebra with no dimension growth.

Keywords

AH-algebra real rank zero stable rank one tracial rank zero dimension growth C*-algebra

Cite

@article{arxiv.1109.2309,
  title  = {A short return to simple AH-algebras with real rank zero},
  author = {Huaxin Lin},
  journal= {arXiv preprint arXiv:1109.2309},
  year   = {2011}
}

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