2009/02/19 by Archey, Dawn
#46L35 #46L40 (Secondary) #46L55 (Primary) 16S35 #FOS: Mathematics #Operator Algebras (math.OA)
paper · doi:10.48550/arxiv.0902.3324
In this paper we introduce an analog of the tracial Rokhlin property, called the \emph projection free tracial Rokhlin property, for C^*-algebras which may not have any nontrivial projections. Using this we show that if A is an infinite dimensional stably finite simple unital C^*-algebra with stable rank one, with strict comparison of positive elements, with only finitely many extreme tracial states, and with the property that every 2-quasi-trace is a trace, and if α is an action of a finite group G with the projection free tracial Rokhlin property, then the crossed product C^*(G, A, α) also has stable rank one (Except there is a mistake in Lemma 3.16, so this is no longer proven)