Zappa-Szép product groupoids and C∗-blends

Authors

Nathan D. Brownlowe, University of WollongongFollow
David Pask, University of WollongongFollow
Jacqui Ramagge, University of SydneyFollow
David I. Robertson, University of WollongongFollow
Michael F. Whittaker, University of GlasgowFollow

RIS ID

105492

Publication Details

Brownlowe, N., Pask, D., Ramagge, J., Robertson, D. & Whittaker, M. F. (2017). Zappa–Szép product groupoids and C∗-blends. Semigroup Forum, 94 (3), 500-519.

Abstract

We study the external and internal Zappa-Szep product of topological groupoids. We show that under natural continuity assumptions the Zappa-Szep product groupoid is etale if and only if the individual groupoids are etale. In our main result we show that the C*-algebra of a locally compact Hausdorff etale Zappa-Szep product groupoid is a C*-blend, in the sense of Exel, of the individual groupoid C*-algebras. We finish with some examples, including groupoids built from *-commuting endomorphisms, and skew product groupoids.