Convolution Algebras of Double Groupoids and Strict 2-Groups

Double groupoids are a type of higher groupoid structure that can arise when one has two distinct groupoid products on the same set of arrows. A particularly important example of such structures is the irrational torus and, more generally, strict 2-groups. Groupoid structures give rise to convolutio...

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Published in:Symmetry, Integrability and Geometry: Methods and Applications
Date:2024
Main Authors: Román, Angel, Villatoro, Joel
Format: Article
Language:English
Published: Інститут математики НАН України 2024
Online Access:https://nasplib.isofts.kiev.ua/handle/123456789/212653
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Journal Title:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Cite this:Convolution Algebras of Double Groupoids and Strict 2-Groups. Angel Román and Joel Villatoro. SIGMA 20 (2024), 093, 26 pages

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
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author Román, Angel
Villatoro, Joel
author_facet Román, Angel
Villatoro, Joel
citation_txt Convolution Algebras of Double Groupoids and Strict 2-Groups. Angel Román and Joel Villatoro. SIGMA 20 (2024), 093, 26 pages
collection DSpace DC
container_title Symmetry, Integrability and Geometry: Methods and Applications
description Double groupoids are a type of higher groupoid structure that can arise when one has two distinct groupoid products on the same set of arrows. A particularly important example of such structures is the irrational torus and, more generally, strict 2-groups. Groupoid structures give rise to convolution operations on the space of arrows. Therefore, a double groupoid comes equipped with two product operations on the space of functions. In this article, we investigate in what sense these two convolution operations are compatible. We use the representation theory of compact Lie groups to get insight into a certain class of 2-groups.
first_indexed 2026-03-21T11:36:49Z
format Article
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institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
issn 1815-0659
language English
last_indexed 2026-03-21T11:36:49Z
publishDate 2024
publisher Інститут математики НАН України
record_format dspace
spelling Román, Angel
Villatoro, Joel
2026-02-09T09:34:33Z
2024
Convolution Algebras of Double Groupoids and Strict 2-Groups. Angel Román and Joel Villatoro. SIGMA 20 (2024), 093, 26 pages
1815-0659
2020 Mathematics Subject Classification: 46L05; 58B34; 46L87; 18G45; 18N10; 58H05
arXiv:2312.00341
https://nasplib.isofts.kiev.ua/handle/123456789/212653
https://doi.org/10.3842/SIGMA.2024.093
Double groupoids are a type of higher groupoid structure that can arise when one has two distinct groupoid products on the same set of arrows. A particularly important example of such structures is the irrational torus and, more generally, strict 2-groups. Groupoid structures give rise to convolution operations on the space of arrows. Therefore, a double groupoid comes equipped with two product operations on the space of functions. In this article, we investigate in what sense these two convolution operations are compatible. We use the representation theory of compact Lie groups to get insight into a certain class of 2-groups.
The authors would like to thank Xiang Tang for some helpful comments on the topic. The authors would like to thank the participants of the Weekend Workshop on Representation Theory and Noncommutative Geometry at Washington University in St. Louis for their valuable feedback and suggestions. The authors would also like to acknowledge the anonymous referee who provided several ideas for improvements to this article. This article is based on work that was supported by the National Science Foundation (Award Numbers 2137999 and 2213097).
en
Інститут математики НАН України
Symmetry, Integrability and Geometry: Methods and Applications
Convolution Algebras of Double Groupoids and Strict 2-Groups
Article
published earlier
spellingShingle Convolution Algebras of Double Groupoids and Strict 2-Groups
Román, Angel
Villatoro, Joel
title Convolution Algebras of Double Groupoids and Strict 2-Groups
title_full Convolution Algebras of Double Groupoids and Strict 2-Groups
title_fullStr Convolution Algebras of Double Groupoids and Strict 2-Groups
title_full_unstemmed Convolution Algebras of Double Groupoids and Strict 2-Groups
title_short Convolution Algebras of Double Groupoids and Strict 2-Groups
title_sort convolution algebras of double groupoids and strict 2-groups
url https://nasplib.isofts.kiev.ua/handle/123456789/212653
work_keys_str_mv AT romanangel convolutionalgebrasofdoublegroupoidsandstrict2groups
AT villatorojoel convolutionalgebrasofdoublegroupoidsandstrict2groups