Noncommutative Geometry and Topology in Prague

The Zappa–Szép product of a Fell bundle by a groupoid

The Zappa–Szép (ZS) product originated as a generalization of the semi-direct product of groups. Keeping in mind the relationship of such semi-direct products to crossed products of C*-algebras, we define an analogue of ZS products for operator algebras: if a groupoid H acts in a sufficiently nice way on a Fell bundle B over G, we construct a new Fell bundle over the ZS product of the groupoids G and H. For this new “ZS Fell bundle”, there is a natural relationship between its representations and those representations of B and H that are covariant in an appropriate sense. Furthermore, this ZS construction lends itself to generalizations of imprimitivity theorems à la Kaliszewski–Muhly–Quigg–Williams.
This talk is based on joint work with Boyu Li (University of Windsor)