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

Huaxin Lin

paper

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

arXiv:math/0401240

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 $T R (A), T R (B) \leq 1$ which satisfy the universal coefficient theorem. We show that $A ≅ B$ if and only if $(K_{0} (A), K_{0} (A)_{+}, [1_{A}], K_{1} (A), T (A)) ≅ (K_{0} (B), K_{0} (B)_{+}, [1_{B}], K_{1} (B), T (B)) .$

Simple nuclear C∗-algebras of tracial topological rank one

Abstract

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