Vol. 6, No. 2, 2021

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On the classification of group actions on C*-algebras up to equivariant KK-equivalence

Ralf Meyer

Vol. 6 (2021), No. 2, 157–238
Abstract

We study the classification of group actions on C-algebras up to equivariant KK-equivalence. We show that any group action is equivariantly KK-equivalent to an action on a simple, purely infinite C*-algebra. We show that a conjecture of Izumi is equivalent to an equivalence between cocycle conjugacy and equivariant KK-equivalence for actions of torsion-free amenable groups on Kirchberg algebras. Let G be a cyclic group of prime order. We describe its actions up to equivariant KK-equivalence, based on previous work by Manuel Köhler. In particular, we classify actions of G on stabilised Cuntz algebras in the equivariant bootstrap class up to equivariant KK-equivalence.

Keywords
universal coefficient theorem, C*-algebra classification, Kirchberg algebra
Mathematical Subject Classification 2010
Primary: 19K35
Secondary: 46L35, 46L80, 46M18
Milestones
Received: 26 June 2019
Revised: 2 November 2020
Accepted: 19 November 2020
Published: 1 August 2021
Authors
Ralf Meyer
Mathematisches Institut
Georg-August Universität
Göttingen
Germany