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Convolution Algebras of Double Groupoids and Strict 2-Groups
Symmetry, integrability and geometry: methods and applications, Tome 20 (2024) Cet article a éte moissonné depuis la source Math-Net.Ru

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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.
Keywords: 2-groups, Haar systems.
Mots-clés : Lie groupoids, convolution, double groupoids 
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     author = {Angel Rom\'an and Joel Villatoro},
     title = {Convolution {Algebras} of {Double} {Groupoids} and {Strict} {2-Groups}},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2024_20_a92/}
}
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Angel Román; Joel Villatoro. Convolution Algebras of Double Groupoids and Strict 2-Groups. Symmetry, integrability and geometry: methods and applications, Tome 20 (2024). http://geodesic.mathdoc.fr/item/SIGMA_2024_20_a92/

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