Zappa-Szép product of a Fell bundle and a groupoid

Abstract

We define the Zappa-Szép product of a Fell bundle by a groupoid, which turns out to be a Fell bundle over the Zappa-Szép product of the underlying groupoids. Under certain assumptions, every Fell bundle over the Zappa-Szép product of groupoids arises in this manner. We then study the representation associated with the Zappa-Szép product Fell bundle and show its relation to covariant representations. Finally, we study the associated universal C*-algebra, which turns out to be a C*-blend, generalizing an earlier result about the Zappa-Szép product of groupoid C*-algebras. In the case of discrete groups, the universal C*-algebra of a Fell bundle embeds injectively inside the universal C*-algebra of the Zappa-Szép product Fell bundle.

36 pages

References in corpus (5)

• Fell bundles over inverse semigroups and twisted etale groupoids
• Coactions and Fell bundles
• Equivalence and Disintegration Theorems for Fell Bundles and their C*-algebras
• Self-Similar $k$-Graph C*-Algebras
• The structure of KMS weights on étale groupoid $C^{\ast }$-algebras

Cited by in corpus (2)

• Wold Decomposition and C*-envelopes of Self-Similar Semigroup Actions on Graphs
• The Imprimitivity Fell Bundle