Rokhlin Dimension and Inductive Limit Actions on AF-algebras

Abstract

Given a separable, AF-algebra A and an inductive limit action on A of a finitely generated abelian group with finite Rokhlin dimension with commuting towers, we give a local description of the associated crossed product C*-algebra. In particular, when A is unital and $\hat{I}\pm \in Aut(A)$ is approximately inner and has the Rokhlin property, we conclude that $A{⋊}_{\hat{I}}\pm \mathbb{Z}$ is an A$\mathbb{T}$-algebra.

Accepted in Annals of Functional Analysis. Corollary 1.8 and its applications in Theorem 2.5 have been improved in response to the referee's comments