Maximal amenable subgroups of arithmetic groups

TL;DR

This paper classifies maximal amenable subgroups within arithmetic groups over global fields, revealing their structure and implications for von Neumann algebras, advancing understanding in algebra and operator algebras.

Contribution

It provides a complete classification of S-maximal amenable subgroups in algebraic groups over global fields and links these to maximal amenable von Neumann subalgebras.

Findings

Classification of S-maximal amenable subgroups up to commensurability

Identification of these subgroups as singular entities

Connection to maximal amenable von Neumann subalgebras

Abstract

By classifying $S$-maximal amenable subgroups of algebraic groups over a global field of characteristic zero, we obtain a complete classification of maximal amenable subgroups up to commensurability in the respective arithmetic groups. Futhermore, we prove that these commensurably maximal amenable subgroups are singular and therefore give rise to maximal amenable von Neumann subalgebras.