Equivalence of Fell Systems and their Reduced C*-Algebras

2011/01/06 by Moutuou, El-kaïoum M., Tu, Jean-Louis
#46L55 #46L80 (Primary) 19L50 (Secondary) #FOS: Mathematics #Functional Analysis (math.FA) #K-Theory and Homology (math.KT) #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.1101.1235

Abstract

This paper is aimed at investigating links between Fell bundles over Morita equivalent groupoids and their corresponding reduced C*-algebras. Mainly, we review the notion of Fell pairs over a Morita equivalence of groupoids, and give the analogue of the Renault's Equivalence Theorem for the reduced C*-algebras of equivalent Fell systems. Eventually, we will use this theorem to connect the reduced C*-algebra of an S¹-central groupoid extension to that of its associated Dixmier-Douady bundle.

Related

• Equivalence and Disintegration Theorems for Fell Bundles and their C*-algebras
• Renault's Equivalence Theorem for Reduced Groupoid C*-algebras
• Some consequences of the stabilization theorem for Fell bundles over exact groupoids
• A Classic Morita Equivalence Result for Fell Bundle C*-algebras
• C^*-algebras of Fell bundles over étale groupoids