There are two very natural products of compact matrix quantum groups: the tensor product and the free product . We define a number of further products interpolating these two. We focus more in detail to the case where is an easy quantum group and , the dual of the cyclic group of order two. We study subgroups of 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 et le produit libre . On définit plusieurs autres produits interpolant ces deux. On étudie en détail le cas où est un groupe “easy” et , le dual du groupe cyclique d’ordre deux. On examine des sous-groupes de 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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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
@article{AIF_2022__72_1_387_0, author = {Gromada, Daniel and Weber, Moritz}, title = {New products and $\protect \mathbb{Z}_2$-extensions of compact matrix quantum groups}, journal = {Annales de l'Institut Fourier}, pages = {387--434}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {72}, number = {1}, year = {2022}, doi = {10.5802/aif.3478}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.3478/} }
TY - JOUR AU - Gromada, Daniel AU - Weber, Moritz TI - New products and $\protect \mathbb{Z}_2$-extensions of compact matrix quantum groups JO - Annales de l'Institut Fourier PY - 2022 SP - 387 EP - 434 VL - 72 IS - 1 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.3478/ DO - 10.5802/aif.3478 LA - en ID - AIF_2022__72_1_387_0 ER -
%0 Journal Article %A Gromada, Daniel %A Weber, Moritz %T New products and $\protect \mathbb{Z}_2$-extensions of compact matrix quantum groups %J Annales de l'Institut Fourier %D 2022 %P 387-434 %V 72 %N 1 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.3478/ %R 10.5802/aif.3478 %G en %F AIF_2022__72_1_387_0
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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