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

Huaxin Lin; Hiroyuki Osaka

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arXiv · math/0601513

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

Huaxin Lin·Hiroyuki Osaka

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Abstract

Let $A$ be a unital simple $A\T$-algebra of real rank zero. Given an isomorphism $γ_1: K_1(A)\to K_1(A),$ 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.

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Huaxin Lin, Hiroyuki Osaka. 2006-01-20. Tracial Rokhlin property for automorphisms on simple $A{\mathbb T}$-algebras. https://arxiv.org/abs/math/0601513

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