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Certain properties for crossed products by automorphisms with a certain non-simple tracial Rokhlin property

Published online by Cambridge University Press:  03 September 2012

XIAOCHUN FANG  and
QINGZHAI FAN
XIAOCHUN FANG
Affiliation:
Department of Mathematics, Shanghai Maritime University, 1550 Haigang Ave, New Harbor City, Shanghai 201306, China (email: qzfan@shmtu.edu.cn) Department of Mathematics, Tongji University, Shanghai 200092, China (email: xfang@mail.tongji.edu.cn)
QINGZHAI FAN
Affiliation:
Department of Mathematics, Shanghai Maritime University, 1550 Haigang Ave, New Harbor City, Shanghai 201306, China (email: qzfan@shmtu.edu.cn)
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Abstract

Let $\Omega $ be a class of unital $C^*$-algebras. Then any simple unital $C^*$-algebra $A\in \mathrm {TA}(\mathrm {TA}\Omega )$ is a $\mathrm {TA}\Omega $ algebra. Let $A\in \mathrm {TA}\Omega $ be an infinite-dimensional $\alpha $-simple unital $C^*$-algebra with the property SP. Suppose that $\alpha :G\to \mathrm {Aut}(A)$ is an action of a finite group $G$ on $A$ which has a certain non-simple tracial Rokhlin property. Then the crossed product algebra $C^*(G,A,\alpha )$ belongs to $\mathrm {TA}\Omega $.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 33 , Issue 5 , October 2013 , pp. 1391 - 1400
Copyright
Copyright © 2012 Cambridge University Press 

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