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

Huaxin Lin

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

Operator Algebras 2007-05-23 v1

Authors: Huaxin Lin

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 $A\cong B.$

Keywords

simple C*-algebras tracial topological rank zero classification Universal Coefficient Theorem K-theory

Cite

@article{arxiv.math/0011079,
  title  = {Classification of simple $C^*$-algebras of tracial topological rank zero},
  author = {Huaxin Lin},
  journal= {arXiv preprint arXiv:math/0011079},
  year   = {2007}
}

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