On the amenable subalgebras of group von Neumann algebras

Abstract

We approach the study of sub-von Neumann algebras of the group von Neumann algebra $L\Gamma$ for countable groups $\Gamma$ from a dynamical perspective. It is shown that $L(\Gamma )$ admits a maximal invariant amenable subalgebra. The notion of invariant probability measures (IRAs) on the space of sub-algebras is introduced, analogous to the concept of Invariant Random Subgroups. And it is shown that amenable IRAs are supported on the maximal amenable invariant sub-algebra.

This final version will appear in the Journal of Functional Analysis

References in corpus (2)

• Charmenability of arithmetic groups of product type
• Subalgebras, subgroups, and singularity

Cited by in corpus (1)

• Invariant $C^{\ast }$-subalgebras of the reduced group $C^{\ast }$-algebra