English

Zappa-Sz\'ep product groupoids and C*-blends

Operator Algebras 2017-06-15 v2

Abstract

We study the external and internal Zappa-Sz\'ep product of topological groupoids. We show that under natural continuity assumptions the Zappa-Sz\'ep 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-Sz\'ep 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

Cite

@article{arxiv.1507.03689,
  title  = {Zappa-Sz\'ep product groupoids and C*-blends},
  author = {Nathan Brownlowe and David Pask and Jacqui Ramagge and David Robertson and Michael F. Whittaker},
  journal= {arXiv preprint arXiv:1507.03689},
  year   = {2017}
}

Comments

Updated to agree with published version

R2 v1 2026-06-22T10:11:13.899Z