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 (New Mexico State University).

Bio: Anna Duwenig earned her PhD from the University of Victoria, Canada, in 2020 under supervision of Heath Emerson and Marcelo Laca. After a 3-year postdoc at the University of Wollongong in Australia, she is now working at KU Leuven in Belgium, where she will soon start an FWO senior postdoctoral fellowship. Her research deals with C*-algebras, with a focus on Cartan subalgebras, Fell bundles, and self-similarity.