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

Huaxin Lin

\newcommand{\CA}{$C^*$-algebra}

We give a classification theorem for unital separable simple nuclear \CA s with tracial topological rank zero which satisfy the Universal Coefficient Theorem. We prove that if $A$ and $B$ are two such \CA s 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 $A\cong B.$