The Rokhlin property vs. Rokhlin dimension 1 on unital Kirchberg algebras

Abstract

We investigate symmetries on unital Kirchberg algebras with respect to the Rokhlin property and finite Rokhlin dimension. In stark contrast to the restrictiveness of the Rokhlin property, every such outer action has Rokhlin dimension at most 1. A consequence of these observations is a relationship between the nuclear dimension of an $\mathcal{O}_\infty$-absorbing C*-algebra and its $\mathcal{O}_2$-stabilization. A more direct and alternative approach to this is given as well. Several applications of this relationship are discussed to cover a fairly large class of $\mathcal{O}_\infty$-absorbing C*-algebras that turn out to have finite nuclear dimension.