Non-supramenable groups acting on locally compact spaces

TL;DR

This paper explores the properties of non-supramenable groups acting on locally compact spaces, linking group properties to the construction of crossed product C*-algebras, including stable Kirchberg algebras.

Contribution

It introduces a new characterization of supramenability via invariant measures and constructs novel crossed product C*-algebras for non-supramenable groups.

Findings

Characterization of supramenability through invariant measures

Construction of stable Kirchberg algebras using crossed products

Extension of crossed product techniques to non-amenable groups

Abstract

Supramenability of groups is characterised in terms of invariant measures on locally compact spaces. This opens the door to constructing interesting crossed product C*-algebras for non-supramenable groups. In particular, stable Kirchberg algebras in the UCT class are constructed using crossed products for both amenable and non-amenable groups.