Z-stability of crossed products by strongly outer actions

Abstract

We consider a certain class of unital simple stably finite C^*-algebras which absorb the Jiang-Su algebra Z tensorially. Under a mild assumption, we show that the crossed product of a C^*-algebra in this class by a strongly outer action of Z^N or a finite group is Z-stable. As an application, we also prove that all strongly outer actions of Z^2 on Z are mutually cocycle conjugate.

Cited by in corpus (8)

• Strongly self-absorbing C*-dynamical systems
• Strongly self-absorbing C*-dynamical systems, III
• Picard groups of certain stably projectionless C*-algebras
• Unitary equivalence of automorphisms of separable C*-algebras
• Trace scaling automorphisms of the stabilized Razak-Jacelon algebra
• Rokhlin dimension: absorption of model actions
• On the bundle of KMS state spaces for flows on a Z-absorbing C*-algebra
• Classification of homomorphisms into simple Z-stable C^*-algebras