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

Abstract

In this paper we introduce an analog of the tracial Rokhlin property, called the {\emph {projection free tracial Rokhlin property}}, for $C^{\ast }$-algebras which may not have any nontrivial projections. Using this we show that if $A$ is an infinite dimensional stably finite simple unital $C^{\ast }$-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 $\alpha$ is an action of a finite group $G$ with the projection free tracial Rokhlin property, then the crossed product $C^{\ast }(G,A,\alpha )$ also has stable rank one (Except there is a mistake in Lemma 3.16, so this is no longer proven)

41 pages, 0 figures. This paper has been withdrawn by the author due to an error in Lemma 3.16. Without this lemma, the main theorem is no longer proven. Current work in progress attempts to prove the main theorem using other methods

References in corpus (5)

• Every simple higher dimensional noncommutative torus is an AT algebra
• Finite cyclic group actions with the tracial Rokhlin property
• The Cuntz semigroup, the Elliott conjecture, and dimension functions on C*-algebras
• The tracial Rokhlin property for actions of finite groups on C*-algebras
• Permutations of Strongly Self-Absorbing C*-algebras

Cited by in corpus (2)

• Freeness of actions of finite groups on C*-algebras
• Crossed Products by Automorphisms with the Tracial Quasi-Rokhlin Property