Zappa-Szép Product of Fell Bundle

Boyu Li

Published 2020-06-04Version 1

We define the Zappa-Sz\'{e}p product of a Fell bundle by a groupoid, which turns out to be a Fell bundle over the Zappa-Sz\'{e}p product of the underlying groupoids. The universal $C^*$-algebra of a Fell bundle is then shown to embed injectively inside the universal $C^*$-algebra of the Zappa-Sz\'{e}p product Fell bundle. We also prove that the universal $C^*$-algebra of the Zappa-Sz\'{e}p product Fell bundle is a $C^*$-blend, generalizing an earlier result on the Zappa-Sz\'{e}p product of groupoid $C^*$-algebras.