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

摘要

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