The Rohlin property for automorphisms on simple C*-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 $A{⋊}_{\alpha }\mathbb{Z}$ has tracial rank zero. We also show that if the induced map ${\alpha }_{\ast 0}$ 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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References in corpus (2)

• Approximate Homotopy of Homomorphisms from $C(X)$ into a Simple $C^{\ast }$-algebra
• Furstenberg transformations on irrational rotation algebras

Cited by in corpus (3)

• The Rokhlin Property for Automorphisms on Simple C*-Algebras
• Tracial Rokhlin property for automorphisms on simple $A\mathbb{T}$-algebras
• Tracial Rokhlin property for actions of amenable groups on C* algebras