Maximal amenable von Neumann subalgebras arising from maximal amenable subgroups

TL;DR

This paper introduces a new criterion based on invariant measures to determine when von Neumann subalgebras from amenable subgroups are maximally amenable, differing from Popa's approach.

Contribution

It provides a general, measure-theoretic criterion for maximal amenability of von Neumann subalgebras from amenable subgroups, using elementary crossed-product computations.

Findings

New criterion for maximal amenability based on invariant measures

Different proof strategy from Popa's central sequences approach

Applicable to subalgebras arising from amenable subgroups

Abstract

We provide a general criterion to deduce maximal amenability of von Neumann subalgebras $L\Lambda \subset L\Gamma$ arising from amenable subgroups $\Lambda$ of discrete countable groups $\Gamma$. The criterion is expressed in terms of $\Lambda$-invariant measures on some compact $\Gamma$-space. The strategy of proof is different from S. Popa's approach to maximal amenability via central sequences [Po83], and relies on elementary computations in a crossed-product C*-algebra.