no. 1
New products and ℤ 2 -extensions of compact matrix quantum groups
[Nouveaux produits et extensions par ℤ 2 pour des groupes quantiques compacts matriciels]
Gromada, Daniel1 ; Weber, Moritz1
1 Saarland University Fachbereich Mathematik Postfach 151150 66041 Saarbrücken (Germany)
Annales de l'Institut Fourier, Tome 72 (2022) no. 1, pp. 387-434.

Il y a deux produits naturels sur des groupes quantiques compacts matriciels : le produit tensoriel G×H et le produit libre G*H. On définit plusieurs autres produits interpolant ces deux. On étudie en détail le cas où G est un groupe “easy” et H=ℤ ^ 2 , le dual du groupe cyclique d’ordre deux. On examine des sous-groupes de G*ℤ ^ 2 en utilisant des catégories des partitions avec des singletons supplémentaires. De nombreux groupes quantiques bistochastiques “non-easy” sont en lien avec avec ces sous-groupes.

There are two very natural products of compact matrix quantum groups: the tensor product G×H and the free product G*H. We define a number of further products interpolating these two. We focus more in detail to the case where G is an easy quantum group and H=ℤ ^ 2 , the dual of the cyclic group of order two. We study subgroups of G*ℤ ^ 2 using categories of partitions with extra singletons. Closely related are many examples of non-easy bistochastic quantum groups.

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Révisé le :
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DOI : 10.5802/aif.3478
Classification : 20G42, 05A18, 18D10
Keywords: quantum group product, two-colored partitions, category of partitions, compact quantum group, tensor category
Mot clés : produit des groupes quantiques, partitions en deux couleurs, catégories des partitions, groupes quantiques compacts, catégorie tensorielles
Gromada, Daniel 1 ; Weber, Moritz 1

1 Saarland University Fachbereich Mathematik Postfach 151150 66041 Saarbrücken (Germany)
Licence : CC-BY-ND 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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     title = {New products and $\protect \mathbb{Z}_2$-extensions of compact matrix quantum groups},
     journal = {Annales de l'Institut Fourier},
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Gromada, Daniel; Weber, Moritz. New products and $\protect \mathbb{Z}_2$-extensions of compact matrix quantum groups. Annales de l'Institut Fourier, Tome 72 (2022) no. 1, pp. 387-434. doi : 10.5802/aif.3478. https://aif.centre-mersenne.org/articles/10.5802/aif.3478/

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