Second cohomology groups of the Hopf * -algebras associated to universal unitary quantum groups
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, Online first, 31 p.

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.

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.

Received:
Revised:
Accepted:
Online First:
DOI: 10.5802/aif.3527
Classification: 16E40,  16T20
Keywords: Hopf * -algebra, cohomology group, compact quantum group.
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) 
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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, Online first, 31 p.

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