Semigroup Forum

, Volume 94, Issue 3, pp 500–519 | Cite as

Zappa–Szép product groupoids and \(C^*\)-blends

  • Nathan Brownlowe
  • David Pask
  • Jacqui Ramagge
  • David Robertson
  • Michael F. Whittaker
Research Article

Abstract

We study the external and internal Zappa–Szép product of topological groupoids. We show that under natural continuity assumptions the Zappa–Szép product groupoid is étale if and only if the individual groupoids are étale. In our main result we show that the \(C^*\)-algebra of a locally compact Hausdorff étale Zappa–Szép 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.

Keywords

\(C^*\)-algebra Groupoid Zappa–Szép product  Skew-product Algebra structure Blend 

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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  • Nathan Brownlowe
    • 1
  • David Pask
    • 1
  • Jacqui Ramagge
    • 2
  • David Robertson
    • 1
  • Michael F. Whittaker
    • 3
  1. 1.School of Mathematics and Applied StatisticsUniversity of WollongongWollongongAustralia
  2. 2.School of Mathematics and StatisticsUniversity of SydneySydneyAustralia
  3. 3.School of Mathematics and StatisticsUniversity of GlasgowGlasgowScotland

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