C*-actions of r-discrete groupoids and inverse semigroups

TL;DR

This paper explores the relationship between groupoid actions on C*-bundles and inverse semigroup actions on C*-algebras, focusing on the case where the groupoid is r-discrete, to deepen understanding of their interplay.

Contribution

It establishes a connection between groupoid actions and inverse semigroup actions in the r-discrete setting, providing new insights into their structural relationship.

Findings

Characterization of groupoid actions on C*-bundles

Correspondence between inverse semigroup actions and groupoid actions

Framework for analyzing r-discrete groupoid actions

Abstract

Groupoid actions on C*-bundles and inverse semigroup actions on C*-algebras are closely related when the groupoid is r-discrete.