Crossed product C*-algebras by finite group actions with the tracial Rokhlin property

Abstract

Let $A$ be a stably finite simple unital $C^{\ast }$-algebra and suppose $\alpha$ is an action of a finite group $G$ with the tracial Rokhlin property. Suppose further $A$ has real rank zero and the order on projections over $A$ is determined by traces. Then the crossed product $C^{\ast }$-algebra $C^{\ast }(G,A,\alpha )$ also has real rank zero and order on projections over $A$ is determined by traces. Moreover, if $A$ also has stable rank one, then $C^{\ast }(G,A,\alpha )$ also has stable rank one.

10 pages, 0 figures. Minor corrections made and typos corrected. To appear in Rocky Mountain Journal of Mathematics

References in corpus (1)

• Finite cyclic group actions with the tracial Rokhlin property