Amenable actions of discrete quantum groups on von Neumann algebras

2018/03/13 by Mohammad S. M. Moakhar, Moakhar, Mohammad S. M. · 1 citation
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.1803.04828

openalex publication_date 2018/03/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 α:\Bbb G\curvearrowright N in terms of \BbbG-injectivity of the von Neumann algebra crossed product N\ltimes_α\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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