Bialgebra cohomology and exact sequences
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 th...
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| Format: | Article |
| Language: | English |
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Académie des sciences
2024-11-01
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| Series: | Comptes Rendus. Mathématique |
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| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.659/ |
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| author | Bichon, Julien |
| author_facet | Bichon, Julien |
| author_sort | Bichon, Julien |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-c9c0cf30e78b417dbd3be5e2ff7b8008 |
| institution | Kabale University |
| issn | 1778-3569 |
| language | English |
| publishDate | 2024-11-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Mathématique |
| spelling | doaj-art-c9c0cf30e78b417dbd3be5e2ff7b80082025-02-07T11:23:50ZengAcadémie des sciencesComptes Rendus. Mathématique1778-35692024-11-01362G111475148310.5802/crmath.65910.5802/crmath.659Bialgebra cohomology and exact sequencesBichon, Julien0Université Clermont Auvergne, CNRS, LMBP, F-63000 Clermont-Ferrand, FranceWe 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.https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.659/Hopf algebrasbialgebra cohomologyYetter–Drinfeld modules |
| spellingShingle | Bichon, Julien Bialgebra cohomology and exact sequences Comptes Rendus. Mathématique Hopf algebras bialgebra cohomology Yetter–Drinfeld modules |
| title | Bialgebra cohomology and exact sequences |
| title_full | Bialgebra cohomology and exact sequences |
| title_fullStr | Bialgebra cohomology and exact sequences |
| title_full_unstemmed | Bialgebra cohomology and exact sequences |
| title_short | Bialgebra cohomology and exact sequences |
| title_sort | bialgebra cohomology and exact sequences |
| topic | Hopf algebras bialgebra cohomology Yetter–Drinfeld modules |
| url | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.659/ |
| work_keys_str_mv | AT bichonjulien bialgebracohomologyandexactsequences |