The Rokhlin Property for Automorphisms on Simple C*-Algebras

Abstract

Let $\mathcal{A}$ be the class of unital separable simple amenable $C$*-algebras $A$ which satisfy the Universal Coefficient Theorem for which $A\otimes M_{\text{P}}$ has tracial rank zero for some supernatural number $\text{p}$ of infinite type. Let $A\in \mathcal{A}$ and let $\alpha$ be an automorphism of $A.$ Suppose that $\alpha$ has the tracial Rokhlin property. Suppose also that there is an integer $J\ge 1$ such that $[α^J]=[\mbox{id}_A]$ in $KL(A,A)$, we show that $A{⋊}_{\alpha }\mathbb{Z}\in \mathcal{A}.$

7 pages

References in corpus (2)

• Crossed products by finite cyclic group actions with the tracial Rokhlin property
• The Rohlin property for automorphisms on simple C*-algebras