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
Datum:2024
Hauptverfasser: Román, Angel, Villatoro, Joel
Format: Artikel
Sprache:Englisch
Veröffentlicht: Інститут математики НАН України 2024
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
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Zusammenfassung: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.
ISSN:1815-0659