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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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2024 |
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2024
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/212653 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | 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| _version_ | 1862566443328995328 |
|---|---|
| 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.
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| first_indexed | 2026-03-21T11:36:49Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-212653 |
| 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 |