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

Abstract

We investigate outer 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 action has Rokhlin dimension at most one. 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. We also give a more direct and alternative approach to this result. 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.