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

Huaxin Lin
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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 $$ (K_0(A), K_0(A)_+, [1_A], K_1(A), T(A)) \cong (K_0(B), K_0(B)_+, [1_B], K_1(B), T(B)). $$

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Huaxin Lin. 2004-11-11. Simple nuclear $C^*$-algebras of tracial topological rank one. https://arxiv.org/abs/math/0401240

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