no. G11
Article de recherche - Algèbre
Bialgebra cohomology and exact sequences
[Cohomologie de bigèbres et suites exactes]
Bichon, Julien1
1Université Clermont Auvergne, CNRS, LMBP, F-63000 Clermont-Ferrand, France
Comptes Rendus. Mathématique, Tome 362 (2024) no. G11, pp. 1475-1483

We show how the bialgebra cohomologies of two Hopf algebras involved in an exact sequence are related, when the third factor is finite-dimensional cosemisimple. As an application, we provide a short proof of the computation of the bialgebra cohomology of the universal cosovereign Hopf algebras in the generic (cosemisimple) case, done recently by Baraquin, Franz, Gerhold, Kula and Tobolski.

Nous montrons comment les cohomologies de Gertstenhaber–Schack de deux algèbres de Hopf imbriquées dans une suite exacte courte sont reliées, quand le troisième facteur est cosemisimple de dimension finie. Nous en déduisons une preuve rapide du calcul de la cohomologie de bigèbre des algèbres de Hopf cosouveraines universelles dans le cas générique, établi récemment par Baraquin, Franz, Gerhold, Kula et Tobolski.

Reçu le :
Révisé le :
Accepté le :
Publié le :
DOI : 10.5802/crmath.659
Classification : 16T05, 16E40
Keywords: Hopf algebras, bialgebra cohomology, Yetter–Drinfeld modules
Mots-clés : Algèbres de Hopf, cohomologie des bigèbres, modules de Yetter–Drinfeld

Bichon, Julien  1

1 Université Clermont Auvergne, CNRS, LMBP, F-63000 Clermont-Ferrand, France
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits
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     pages = {1475--1483},
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Bichon, Julien. Bialgebra cohomology and exact sequences. Comptes Rendus. Mathématique, Tome 362 (2024) no. G11, pp. 1475-1483. doi: 10.5802/crmath.659

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