Vol. 313, No. 1, 2021

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Convolution algebras for relational groupoids and reduction

Ivan Contreras, Nima Moshayedi and Konstantin Wernli

Vol. 313 (2021), No. 1, 75–102
DOI: 10.2140/pjm.2021.313.75
Abstract

We introduce the notions of relational groupoids and relational convolution algebras. We provide various examples arising from the group algebra of a group G and a given normal subgroup H. We also give conditions for the existence of a Haar system of measures on a relational groupoid compatible with the convolution, and we prove a reduction theorem that recovers the usual convolution of a Lie groupoid.

Keywords
convolution algebra, Lie groupoids, Haar systems, relational groupoids, reduction
Mathematical Subject Classification
Primary: 18B10, 18B40, 20L05, 57R56
Milestones
Received: 19 August 2020
Revised: 14 January 2021
Accepted: 6 May 2021
Published: 17 September 2021
Authors
Ivan Contreras
Department of Mathematics and Statistics
Amherst College
Amherst, MA
United States
Nima Moshayedi
Department of Mathematics
University of California, Berkeley
Berkeley, CA
United States
Konstantin Wernli
Department of Mathematics and Computer Science
University of Southern Denmark
Odense
Denmark