Operator algebra seminar

Speaker:  Selcuk Barlak (University of Southern Denmark)

Title: Finite, abelian group actions on Kirchberg algebras

Abstract: I will talk about two joint projects with X. Li and G. Szabó, respectively. First, I will present a characterization of the UCT for crossed products of unital UCT Kirchberg algebras by certain outer finite cyclic group actions that are approximately representable in the sense of Izumi. As I will explain, this involves a quasi-freeness-type condition for the actions. This result also leads to a new characterization of the UCT problem for separable, nuclear C*-algebras. We then turn to finite, abelian group actions on purely infinite, simple Cuntz-Krieger algebras by certain quasi-free automorphisms. The main result of the second part states that for many such actions approximate representability, or at least Izumi's weaker notion of strong approximate innerness, holds. In combination with a result by Izumi, this leads to a classification of such actions, provided the Cuntz-Krieger algebras are (possibly non-canonically) isomorphic to O_2.