Simple nuclear $C^*$-algebras of tracial topological rank one

Huaxin Lin

Simple nuclear $C^*$-algebras of tracial topological rank one

Operator Algebras 2007-05-23 v5

Authors: Huaxin Lin

Abstract

We give a classification theorem for unital separable nuclear simple \CA s with tracial rank no more than one. Let $A$ and $B$ be two unital separable simple nuclear \CA s with $TR(A), TR(B)\le 1$ which satisfy the universal coefficient theorem. We show that $A\cong B$ if and only if $(K_0(A), K_0(A)_+, [1_A], K_1(A), T(A)) \cong (K_0(B), K_0(B)_+, [1_B], K_1(B), T(B)).$

Keywords

simple nuclear c*-algebras tracial topological rank classification universal coefficient theorem k-theory

Cite

@article{arxiv.math/0401240,
  title  = {Simple nuclear $C^*$-algebras of tracial topological rank one},
  author = {Huaxin Lin},
  journal= {arXiv preprint arXiv:math/0401240},
  year   = {2007}
}

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