Existence of the Matui-Sato tracial Rokhlin property

Abstract

We show by construction that when $G$ is an elementary amenable group and $A$ is a unital simple nuclear and tracially approximately divisible $C^{\ast }$-algebra, there exists an action $\omega$ of $G$ on $A$ with the tracial Rokhlin property in the sense of Matui and Sato. In particular, group actions with this Matui-Sato tracial Rokhlin property always exist for unital simple separable nuclear $C^{\ast }$-algebras with tracial rank at most one. If $A$ is simple with rational tracial rank at most one, then the crossed product $A{⋊}_{\omega }G$ is also simple with rational tracial rank at most one.

arXiv comment21 pages. Results for crossed products updated to reflect Osawa-Rordam-Sato's recent work. Exposition simplified and title changed. To appear in the Journal of Operator Theory

References in corpus (1)

• Tensor Products of Classifiable C*-algebras

Cited by in corpus (1)

• Strongly outer product type actions