The Rohlin property for automorphisms on simple C*-algebras

Details The Rohlin property for automorphisms on simple C*-algebras The Rohlin property for automorphisms on simple C*-algebras

2006-02-23

arxiv.org/abs/math/0602513v2

Mathematics

Operator Algebras

An error was found and correction was made in this revision

Scientific paper

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.

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