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On
the classification of group actions on C*-algebras up to
equivariant KK-equivalence
Ralf Meyer |
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Vol. 6 (2021), No. 2, 157–238
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Abstract |
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We study the classification of group actions on -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 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 on stabilised Cuntz algebras in the equivariant bootstrap class up to equivariant KK-equivalence. |
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Keywords
universal coefficient theorem, C*-algebra classification,
Kirchberg algebra
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Mathematical Subject Classification 2010
Primary: 19K35
Secondary: 46L35, 46L80, 46M18
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Milestones
Received: 26 June 2019
Revised: 2 November 2020
Accepted: 19 November 2020
Published: 1 August 2021
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Authors |
| Ralf Meyer | |
| Mathematisches Institut Georg-August Universität Göttingen Germany |
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