Rokhlin actions and self-absorbing C^∗-algebras

Ilan Hirshberg and Wilhelm Winter

Vol. 233 (2007), No. 1, 125–143

DOI: 10.2140/pjm.2007.233.125

Abstract

Let 𝒜 be a unital separable C^∗-algebra and 𝒟 a K₁-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 satisfies a Rokhlin property. In the case of a compact Rokhlin action we prove a similar statement about approximate divisibility.

Keywords

self-absorbing, approximately inner half-flip, crossed products, Rokhlin property

Mathematical Subject Classification 2000

Primary: 46L05, 46L55

Milestones

Received: 15 May 2006

Revised: 22 June 2007

Accepted: 25 June 2007

Published: 1 November 2007