-algebras of Tracial Topological Rank One *
نویسنده
چکیده
We give a classification theorem for unital separable nuclear simple C∗-algebras with tracial rank no more than one. Let A and B be two unital separable simple nuclear C∗-algebras with TR(A), TR(B) ≤ 1 which satisfy the universal coefficient theorem. We show that A ∼= B if and only if there is an order and unit preserving isomorphism γ = (γ0, γ1, γ2) : (K0(A),K0(A)+, [1A],K1(A), T (A)) ∼= (K0(B),K0(B)+, [1B ],K1(B), T (B)), where γ 2 (τ )(x) = τ (γ0(x)) for each x ∈ K0(A) and τ ∈ T (B).
منابع مشابه
20 04 Simple nuclear C ∗ - algebras of tracial topological rank one ∗
We give a classification theorem for unital separable nuclear simple C∗-algebras with tracial rank no more than one. Let A and B be two unital separable simple nuclear C∗-algebras with TR(A), TR(B) ≤ 1 which satisfy the universal coefficient theorem. We show that A ∼= B if and only if (K0(A),K0(A)+, [1A], K1(A), T (A)) ∼= (K0(B), K0(B)+, [1B ], K1(B), T (B)).
متن کاملClassification of Simple C * -algebras of Tracial Topological
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 (K0(A),K0(A)+, [1A], K1(A)) = (K0(B), K0(B)+, [1B ], K1(B)), then A = B.
متن کاملThe Rokhlin property and the tracial topological rank
Let A be a unital separable simple C∗-algebra with TR(A) ≤ 1 and α be an automorphism. We show that if α satisfies the tracially cyclic Rokhlin property then TR(A ⋊α Z) ≤ 1. We also show that whenever A has a unique tracial state and αm is uniformly outer for each m and αr is approximately inner for some r > 0, α satisfies the tracial cyclic Rokhlin property. By applying the classification theo...
متن کاملReal structure in unital separable simple C*-algebras with tracial rank zero and with a unique tracial state
Let A be a simple unital C∗-algebra with tracial rank zero and with a unique tracial state and let Φ be an involutory ∗-antiautomorphism of A. It is shown that the associated real algebra AΦ = {a ∈ A : Φ(a) = a∗} also has tracial rank zero. Let A be a unital simple separable C∗-algebra with tracial rank zero and suppose that A has a unique tracial state. If Φ is an involutory ∗-antiautomorphism...
متن کاملOn the Classification of Simple Z-stable C-algebras with Real Rank Zero and Finite Decomposition Rank
We show that, if A is a separable simple unital C-algebra which absorbs the Jiang–Su algebra Z tensorially and which has real rank zero and finite decomposition rank, then A is tracially AF in the sense of Lin, without any restriction on the tracial state space. As a consequence, the Elliott conjecture is true for the class of C-algebras as above which, additionally, satisfy the Universal Coeff...
متن کامل