Convolution Algebras For Relational Groupoids And Reduction

Ivan Contreras*, Nima Moshayedi, Konstantin Wernli

*Kontaktforfatter

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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.

OriginalsprogEngelsk
TidsskriftPacific Journal of Mathematics
Vol/bind313
Udgave nummer1
Sider (fra-til)75-102
Antal sider28
ISSN0030-8730
DOI
StatusUdgivet - 2021

Bibliografisk note

Funding Information:
We would like to thank Iakovos Androulidakis, Alberto Cattaneo, Eli Hawkins, Rajan Mehta, and Michele Schiavina for useful discussions and comments on the manuscript. We also thank the anonymous referee for their useful and detailed comments. Moshayedi was supported by the NCCR SwissMAP, by the Swiss National Science Foundation, and by the SNF grant No. 200020_192080. Moshayedi would like to thank the University of Illinois Urbana–Champaign for hospitality, where this work started. Wernli would like to thank the University of Zürich, where a part of this work was written, and acknowledges partial support by NCCR SwissMAP, by the Swiss National Science Foundation, by the European Cooperation in Science and Technology (COST), by the COST Action MP1405 QSPACE, and by the SNF grant No. 200020 172498/1 during his affiliation with the University of Zurich. Wernli acknowledges further support from a BMS Dirichlet postdoctoral fellowship and the SNF Postdoc Mobility grant P2ZHP2_184083, and he would like to thank the Humboldt-Universität Berlin, in particular the group of Dirk Kreimer, and the University of Notre Dame for their hospitality.

Publisher Copyright:
© 2021. Pacific Journal of Mathematics. All rights reserved.

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