New products and 2 -extensions of compact matrix quantum groups
Annales de l'Institut Fourier, Volume 72 (2022) no. 1, pp. 387-434.

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= ^ 2 , the dual of the cyclic group of order two. We study subgroups of G* ^ 2 using categories of partitions with extra singletons. Closely related are many examples of non-easy bistochastic quantum groups.

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= ^ 2 , le dual du groupe cyclique d’ordre deux. On examine des sous-groupes de G* ^ 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.

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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)
License: CC-BY-ND 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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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, Volume 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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