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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 745369, 10 pages
http://dx.doi.org/10.1155/2012/745369
Research Article

The Tracial Class Property for Crossed Products by Finite Group Actions

1Department of Mathematics, Zhejiang Normal University, Zhejiang, Jinhua 321004, China
2Department of Mathematics, Tongji University, Shanghai 200092, China

Received 11 September 2012; Accepted 14 October 2012

Academic Editor: Toka Diagana

Copyright © 2012 Xinbing Yang and Xiaochun Fang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We define the concept of tracial -algebra of -algebras, which generalize the concept of local -algebra of -algebras given by H. Osaka and N. C. Phillips. Let be any class of separable unital -algebras. Let be an infinite dimensional simple unital tracial -algebra with the (SP)-property, and let be an action of a finite group on which has the tracial Rokhlin property. Then is a simple unital tracial -algebra.