Maximal amenable subalgebras of von Neumann algebras associated with hyperbolic groups

Abstract

We prove that for any infinite, maximal amenable subgroup $H$ in a hyperbolic group $G$, the von Neumann subalgebra $LH$ is maximal amenable inside $LG$. It provides many new, explicit examples of maximal amenable subalgebras in II${}_1$ factors. We also prove similar maximal amenability results for direct products of relatively hyperbolic groups and orbit equivalence relations arising from measure-preserving actions of such groups.

16 pages, 2 figures, new section added about direct products. Accepted for publication to Mathematische Annalen

References in corpus (4)

• A class of $\mathrm{I}{\mathrm{I}}_1$ factors with an exotic abelian maximal amenable subalgebra
• Structure of $\mathrm{I}{\mathrm{I}}_1$ factors arising from free Bogoljubov actions of arbitrary groups
• The cup subalgebra of a II_1 factor given by a subfactor planar algebra is maximal amenable
• Maximal injective and mixing masas in group factors

Cited by in corpus (1)

• The cup subalgebra has the absorbing amenability property