Skip to main content
placeholder image

Zappa–Szép product groupoids and C∗-blends

Journal 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 C*-commuting endomorphisms, and skew product groupoids.

Authors


  •   Brownlowe, Nathan D. (external author)
  •   Pask, David A.
  •   Ramagge, Jacqui
  •   Robertson, Dave I. (external author)
  •   Whittaker, Michael F. (external author)

Publication Date


  • 2017

Citation


  • 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.

Scopus Eid


  • 2-s2.0-84957550844

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/5981

Number Of Pages


  • 19

Start Page


  • 500

End Page


  • 519

Volume


  • 94

Issue


  • 3

Place Of Publication


  • United States

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 C*-commuting endomorphisms, and skew product groupoids.

Authors


  •   Brownlowe, Nathan D. (external author)
  •   Pask, David A.
  •   Ramagge, Jacqui
  •   Robertson, Dave I. (external author)
  •   Whittaker, Michael F. (external author)

Publication Date


  • 2017

Citation


  • 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.

Scopus Eid


  • 2-s2.0-84957550844

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/5981

Number Of Pages


  • 19

Start Page


  • 500

End Page


  • 519

Volume


  • 94

Issue


  • 3

Place Of Publication


  • United States