Ideals in Cross Sectional C*-algebras of Fell Bundles

TL;DR

This paper explores the relationship between the ideal structure of cross-sectional C*-algebras of Fell bundles and the dynamics of associated partial group actions on spectra, providing new insights into their algebraic properties.

Contribution

It introduces a framework linking the ideal structure of cross-sectional C*-algebras to the dynamics of partial actions on spectra, advancing understanding of Fell bundles over discrete groups.

Findings

Characterization of ideals via partial action dynamics

Analysis of full and reduced cross-sectional C*-algebras

Connection between algebraic structure and dynamical systems

Abstract

With each Fell bundle over a discrete group G we associate a partial action of G on the spectrum of the unit fiber. We discuss the ideal structure of the corresponding full and reduced cross-sectional C*-algebras in terms of the dynamics of this partial action.