Integrability of dual coactions on Fell bundle C*-algebras

TL;DR

This paper investigates the integrability of dual coactions on Fell bundle C*-algebras, establishing that such coactions are integrable for all locally compact groups, thus extending previous results from abelian to general groups.

Contribution

It proves that dual coactions on C*-algebras of Fell bundles are integrable for all locally compact groups, broadening the scope of prior work on abelian groups.

Findings

Dual coactions on Fell bundle C*-algebras are integrable.

Generalization of integrability results from abelian to all locally compact groups.

Strengthens the connection between coactions and Fell bundles.

Abstract

We study integrability for coactions of locally compact groups. For abelian groups, this corresponds to integrability of the associated action of the Pontrjagin dual group. The theory of integrable group actions has been previously studied by Ruy Exel, Ralf Meyer and Marc Rieffel. Our goal is to study the close relationship between integrable group coactions and Fell bundles. As a main result, we prove that dual coactions on C*-algebras of Fell bundles are integrable, generalizing results by Ruy Exel for abelian groups.