On Fell bundles over inverse semigroups and their left regular representations

TL;DR

This paper extends Wordingham's theorem to Fell bundles over inverse semigroups, analyzing their left regular representations and the related cross-sectional C*-algebras.

Contribution

It introduces a generalized version of Wordingham's theorem for Fell bundles over inverse semigroups and explores implications for associated C*-algebras.

Findings

Generalized Wordingham's theorem established

Analysis of cross-sectional C*-algebras provided

Insights into representations of Fell bundles obtained

Abstract

We prove a version of Wordingham's theorem for left regular representations in the setting of Fell bundles of inverse semigroups and use this result to discuss the various associated cross sectional C*-algebras.