CLASSIFICATION OF SIMPLE C^{∗}-ALGEBRAS OF TRACIAL TOPOLOGICAL RANK ZERO

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))
≅ (K_{0}(B), K_{0}(B)_{+}, [1_{B}], K_{1}(B)),

then A ≅ B.