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

Published online by Cambridge University Press:  01 August 2008

HUAXIN LIN and
HIROYUKI OSAKA
HUAXIN LIN
Affiliation:
Department of Mathematics, East China Normal University, Shanghai, ChinaUniversity of Oregon, Eugene, Oregon 97403-1222, USA
HIROYUKI OSAKA
Affiliation:
Department of Mathematical Sciences, Ritsumeikan University, Kusatsu, Shiga, 525-8577, Japan
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Abstract

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Let A be a unital simple $A\mathbb {T}$-algebra of real rank zero. Given an isomorphismγ1:K1(A)→K1(A), we show that there is an automorphism α:A→A such that α*1=γ1 and α has the tracial Rokhlin property. Consequently, the crossed product $A\rtimes _{\alpha }\mathbb {Z}$ is a simple unital AH-algebra with real rank zero. We also show that automorphisms with the Rokhlin property can be constructed from minimal homeomorphisms on a connected compact metric space.

Information

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 28 , Issue 4 , August 2008, pp. 1215 - 1241
Copyright
Copyright © 2008 Cambridge University Press

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