Local tracial C*-algebras

Document Type: Research Paper

Authors

Department of Mathematics‎, ‎Shanghai Maritime University‎, ‎Shanghai 200135‎, ‎China.

Abstract

‎Let $\Omega$ be a class of unital‎ ‎$C^*$-algebras‎. ‎We introduce the notion of a local tracial $\Omega$-algebra‎. ‎Let $A$ be an $\alpha$-simple unital local tracial $\Omega$-algebra‎. ‎Suppose that $\alpha:G\to$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 ‎$C^*(G,A,\alpha)$ is a unital local tracial $\Omega$-algebra.

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Main Subjects

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History

• Receive Date: 02 May 2015
• Revise Date: 12 October 2015
• Accept Date: 14 February 2017