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The Rohlin property for automorphisms on simple C*-algebras

Research paper by Huaxin Lin

Indexed on: 27 Jan '10Published on: 27 Jan '10Published in: Mathematics - Operator Algebras



Abstract

We study a general Kishimoto's problem for automorphisms on simple C*-algebras with tracial rank zero. Let $A$ be a unital separable simple C*-algebra with tracial rank zero and let $\alpha$ be an automorphism. Under the assumption that $\alpha$ has certain Rokhlin property, we present a proof that $A\rtimes_{\alpha}\Z$ has tracial rank zero. We also show that if the induced map $\alpha_{*0}$ on $K_0(A)$ fixes a "dense" subgroup of $K_0(A)$ then the tracial Rokhlin property implies a stronger Rokhlin property. Consequently, the induced crossed product C*-algebras have tracial rank zero.