Simple C*-algebras with Locally Bounded Irreducible Representation

Let A and B be two unital separable simple nuclear C*-algebras with tracial topological rank zero. Suppose that both A and B have the local approximation property: for any finite subset F and ε>0, there is a C*-subalgebra C such that its dimensions of irreducible representations are bounded anddist(x, C)<ε for all x∈F. Suppose also that ρA(K0(A)) is a divisible group, where ρA: K0(A)→Aff(T(A)) is the homomorphism from K0(A) to affine functions on the tracial space of A. Then A≅B if and only if(K0(A), K0(A)+, [1A], K1(A))≅(K0(B), K0(B)+, [1B], K 1(B)). Applications to simple crossed products arising from smooth minimal dynamical systems are given. Let M1 and M2 be compact manifolds, hi: Mi→Mi be a minimal diffeomorphism (i=1, 2) and let Ai=C*(Z, Mi, hi). Suppose that TR(Ai)=0 and the range of K0(Ai) in Aff(T(Ai)) is divisible. Then A1≅A2 if and only if(K0(A1), K0(A 1), [1A1], K0(A1)))≅(K0(A2), K0(A2)+, [1A2], K1(A2)).