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 . 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 . Dans ce cadre nous sommes obligés d’utiliser des représentations de dimension infinie pour la construction des cocycles.
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Keywords: Hopf -algebra, cohomology group, compact quantum group.
@unpublished{AIF_0__0_0_A105_0, author = {Das, Biswarup and Franz, Uwe and Kula, Anna and Skalski, Adam}, title = {Second cohomology groups of the {Hopf}$^*$-algebras associated to universal unitary quantum groups}, journal = {Annales de l'Institut Fourier}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, year = {2022}, doi = {10.5802/aif.3527}, language = {en}, note = {Online first}, }
TY - UNPB AU - Das, Biswarup AU - Franz, Uwe AU - Kula, Anna AU - Skalski, Adam TI - Second cohomology groups of the Hopf$^*$-algebras associated to universal unitary quantum groups JO - Annales de l'Institut Fourier PY - 2022 DA - 2022/// PB - Association des Annales de l’institut Fourier N1 - Online first UR - https://doi.org/10.5802/aif.3527 DO - 10.5802/aif.3527 LA - en ID - AIF_0__0_0_A105_0 ER -
%0 Unpublished Work %A Das, Biswarup %A Franz, Uwe %A Kula, Anna %A Skalski, Adam %T Second cohomology groups of the Hopf$^*$-algebras associated to universal unitary quantum groups %J Annales de l'Institut Fourier %D 2022 %I Association des Annales de l’institut Fourier %Z Online first %U https://doi.org/10.5802/aif.3527 %R 10.5802/aif.3527 %G en %F AIF_0__0_0_A105_0
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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