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