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

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

2009-02-17

arxiv.org/abs/0902.2865v2

Mathematics

Operator Algebras

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

Scientific paper

Let $A$ be a stably finite simple unital $C^*$-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 $C^*$-algebra $C^*(G,A, \alpha)$ also has real rank zero and order on projections over $A$ is determined by traces. Moreover, if $A$ also has stable rank one, then $C^*(G,A, \alpha)$ also has stable rank one.

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