Zappa-Szép product groupoids and C*-blends

Brownlowe, N., Pask, D., Ramagge, J., Robertson, D. and Whittaker, M. (2017) Zappa-Szép product groupoids and C*-blends. Semigroup Forum, 94(3), pp. 500-519. (doi:10.1007/s00233-016-9775-z)

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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∗C∗-algebra of a locally compact Hausdorff étale Zappa–Szép product groupoid is a C∗C∗-blend, in the sense of Exel, of the individual groupoid C∗C∗-algebras. We finish with some examples, including groupoids built from ∗∗-commuting endomorphisms, and skew product groupoids.

Item Type:Articles
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Whittaker, Dr Michael
Authors: Brownlowe, N., Pask, D., Ramagge, J., Robertson, D., and Whittaker, M.
Subjects:Q Science > QA Mathematics
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Research Group:Analysis
Journal Name:Semigroup Forum
Publisher:Springer US
ISSN:0037-1912
ISSN (Online):1432-2137
Published Online:05 February 2016
Copyright Holders:Copyright © 2016 Springer Science+Business Media New York
First Published:First published in Semigroup Forum 94(3):500-519
Publisher Policy:Reproduced in accordance with the copyright policy of the publisher

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