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Equivariant $\mathcal {O}_{2}$-absorption theorem for exact groups

Part of: Selfadjoint operator algebras

Published online by Cambridge University Press:  17 June 2021

Yuhei Suzuki
Yuhei Suzuki*
Affiliation:
Department of Mathematics, Faculty of Science, Hokkaido University, Kita 10, Nishi 8, Kita-Ku, Sapporo, Hokkaido060-0810, Japanyuhei@math.sci.hokudai.ac.jp
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Abstract

We show that, up to strong cocycle conjugacy, every countable exact group admits a unique equivariantly $\mathcal {O}_{2}$-absorbing, pointwise outer action on the Cuntz algebra $\mathcal {O}_{2}$ with the quasi-central approximation property (QAP). In particular, we establish the equivariant analogue of the Kirchberg $\mathcal {O}_{2}$-absorption theorem for these groups.

Keywords

C*-dynamical systemsstrong cocycle conjugacyamenable actions

MSC classification

Primary: 46L55: Noncommutative dynamical systems
Secondary: 46L05: General theory of $C^*$-algebras
Type
Research Article
Information
Compositio Mathematica , Volume 157 , Issue 7 , July 2021 , pp. 1492 - 1506
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Copyright
© 2021 The Author(s). The publishing rights in this article are licensed to Foundation Compositio Mathematica under an exclusive licence

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