Rokhlin actions and self-absorbing C*-algebras

TL;DR

This paper demonstrates that under certain conditions, the property of D-absorption in a unital separable C*-algebra is preserved when taking crossed products by specific groups, given the action satisfies a Rokhlin property.

Contribution

It establishes that D-absorption is preserved under crossed products by compact groups, Z, or R for actions with Rokhlin properties, extending known permanence results.

Findings

Crossed products by compact groups, Z, or R preserve D-absorption under Rokhlin actions.

Rokhlin actions imply approximate divisibility preservation.

Results apply to strongly self-absorbing C*-algebras with K_1-injectivity.

Abstract

Let A be a unital separable C*-algebra, and D a K_1-injective strongly self-absorbing C*-algebra. We show that if A is D-absorbing, then the crossed product of A by a compact second countable group or by Z or by R is D-absorbing as well, assuming the action satisfying a Rokhlin property. In the case of a compact Rokhlin action we prove a similar statement about approximate divisibility.