Supramenable groups and partial actions

TL;DR

This paper characterizes supramenable groups through invariant measures and tracial states in partial actions, revealing limitations and conditions for decomposing partial crossed products of C*-algebras.

Contribution

It provides new characterizations of supramenability via partial actions and explores conditions for decomposing partial crossed products.

Findings

Supramenability characterized by invariant measures and tracial states.

Decomposition of partial crossed products is not always possible.

Conditions for successful decomposition are identified.

Abstract

We characterize supramenable groups in terms of existence of invariant probability measures for partial actions on compact Hausdorff spaces and existence of tracial states on partial crossed products. These characterizations show that, in general, one cannot decompose a partial crossed product of a C*-algebra by a semi-direct product of groups as two iterated partial crossed products. We give conditions which ensure that such decomposition is possible.