no. 2
Second cohomology groups of the Hopf * -algebras associated to universal unitary quantum groups
[Deuxièmes groupes de cohomologie des algèbres de Hopf involutives associées aux groupes quantiques unitaires universels]
Das, Biswarup1 ; Franz, Uwe2 ; Kula, Anna1 ; Skalski, Adam3
1 Instytut Matematyczny, Uniwersytet Wrocławski, pl.Grunwaldzki 2, 50-384 Wrocław (Poland)
2 Laboratoire de mathématiques de Besançon, Université de Bourgogne Franche-Comté, 16, route de Gray, 25030 Besançon cedex (France)
3 Institute of Mathematics of the Polish Academy of Sciences, ul. Śniadeckich 8, 00–656 Warszawa (Poland)
Annales de l'Institut Fourier, Tome 73 (2023) no. 2, pp. 479-509.

Nous calculons les deuxièmes (et premiers) groupes de cohomologi des algèbres involutives associées aux groupes quantiques unitaires universels pas nécessairement du type Kac, étendant ainsi nos résultats précédents pour le groupe unitaire libre U d + . Dans ce cadre nous sommes obligés d’utiliser des représentations de dimension infinie pour la construction des cocycles.

We compute the second (and the first) cohomology groups of * -algebras associated with the universal quantum unitary groups of not necessarily Kac type, extending our earlier results for the free unitary group U d + . The extended setup forces us to use infinite-dimensional representations to construct the cocycles.

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Révisé le :
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DOI : 10.5802/aif.3527
Classification : 16E40, 16T20
Keywords: Hopf $^*$-algebra, cohomology group, compact quantum group.
Mot clés : Algèbre de Hopf involutive, groupe de cohomologie, groupe quantique compact.
Das, Biswarup 1 ; Franz, Uwe 2 ; Kula, Anna 1 ; Skalski, Adam 3

1 Instytut Matematyczny, Uniwersytet Wrocławski, pl.Grunwaldzki 2, 50-384 Wrocław (Poland)
2 Laboratoire de mathématiques de Besançon, Université de Bourgogne Franche-Comté, 16, route de Gray, 25030 Besançon cedex (France)
3 Institute of Mathematics of the Polish Academy of Sciences, ul. Śniadeckich 8, 00–656 Warszawa (Poland)
Licence : CC-BY-ND 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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     title = {Second cohomology groups of the {Hopf}$^*$-algebras associated to universal unitary quantum groups},
     journal = {Annales de l'Institut Fourier},
     pages = {479--509},
     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
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Das, Biswarup; Franz, Uwe; Kula, Anna; Skalski, Adam. Second cohomology groups of the Hopf$^*$-algebras associated to universal unitary quantum groups. Annales de l'Institut Fourier, Tome 73 (2023) no. 2, pp. 479-509. doi : 10.5802/aif.3527. https://aif.centre-mersenne.org/articles/10.5802/aif.3527/

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