Tracial Rokhlin property for automorphisms on simple $A\mathbb{T}$-algebras

Abstract

Let $A$ be a unital simple $A\T$-algebra of real rank zero. Given an isomorphism ${\gamma }_1:K_1(A)\to K_1(A),$ we show that there is an automorphism $\af: A\to A$ such that $\af_{*1}=γ_1$ which has the tracial Rokhlin property. Consequently, the crossed product $A\rtimes_{\af}\Z$ is a simple unital AH-algebra with real rank zero. We also show that automorphism with Rokhlin property can be constructed from minimal homeomorphisms on a connected compact metric space.

References in corpus (2)

• Crossed products by finite cyclic group actions with the tracial Rokhlin property
• Minimal Homeomorphisms and Approximate Conjugacy in Measure