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Amenable actions of discrete quantum groups on von Neumann algebras

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arxiv 1803.04828 v2 pith:2CSVCBT4 submitted 2018-03-13 math.OA

Mohammad S. M. Moakhar This is my paper · ORCID
classification math.OA
keywords actionsdiscreteneumannquantumalgebrasalphaamenabilityamenable
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abstract

We introduce the notion of Zimmer amenability for actions of discrete quantum groups on von Neumann algebras. We prove generalizations of several fundamental results of the theory in the noncommutative case. In particular, we give a characterization of Zimmer amenability of an action $\alpha:\Bbb G\curvearrowright N$ in terms of $\hat{\Bbb{G}}$-injectivity of the von Neumann algebra crossed product $N\ltimes_\alpha\Bbb G$. As an application we show that the actions of any discrete quantum group on its Poisson boundaries are always amenable.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Braided tensor product of von Neumann algebras

    math.OA 2024-12 conditional novelty 8.0 of 10

    Braided tensor products of von Neumann algebras are constructed for actions of locally compact quantum groups linked by a bicharacter, with a canonical action in the quasi-triangular case and with crossed products as ...

  2. Fej\'er representations for discrete quantum groups and applications

    math.OA 2025-02 conditional novelty 6.0 of 10

    A discrete quantum group has the approximation property exactly when every element of its C*- or von Neumann crossed products has a Fejér-type series representation.

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