Classification of simple $C^*$-algebras of tracial topological rank zero

Huaxin Lin

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Classification of simple $C^*$-algebras of tracial topological rank zero

Huaxin Lin

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Abstract

We give a classification theorem for unital separable simple nuclear $C^*$-algebras with tracial topological rank zero which satisfy the Universal Coefficient Theorem. We prove that if $A$ and $B$ are two such $C^*$-algebras and $$ (K_0(A), K_0(A)_+, [1_A], K_1(A)) $$ $$ \cong (K_0(B), K_0(B)_+, [1_B], K_1(B)), $$ then $A\cong B.$

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BibTeX RIS

Huaxin Lin. 2000-11-13. Classification of simple $C^*$-algebras of tracial topological rank zero. https://arxiv.org/abs/math/0011079

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