Discrete amenable group actions on von Neumann algebras and invariant nuclear C*-subalgebras

Abstract

Let $G$ be a countable discrete amenable group, $\mathcal{M}$ a McDuff factor von Neumann algebra, and $A$ a separable nuclear weakly dense C${}^{\ast }$-subalgebra of $\mathcal{M}$. We show that if two centrally free actions of $G$ on $\mathcal{M}$ differ up to approximately inner automorphisms then they are outer conjugate by an approximately inner automorphism, in the operator norm topology, which makes $A$ invariant. In addition, when $A$ is unital, simple, and with a unique tracial state and $\alpha$ is an automorphism of $A$ we also show that the aperiodicity of $\alpha$ on the von Neumann algebra is equivalent to the weak Rohlin property.

12 pages

References in corpus (2)

• A generalization of the Jiang-Su construction
• Unified approach to classification of actions of discrete amenable groups on injective factors