On the finite generation of the cohomology of abelian extensions of Hopf algebras
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909246378999808 |
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| author | Andruskiewitsch, Nicolás Natale, Sonia |
| author_facet | Andruskiewitsch, Nicolás Natale, Sonia |
| contents | A finite-dimensional Hopf algebra is called quasi-split if it is Morita equivalent to a split abelian extension of Hopf algebras. Combining results of Schauenburg and Negron, it is shown that every quasi-split finite-dimensional Hopf algebra satisfies the finite generation cohomology conjecture of Etingof and Ostrik. This is applied to a family of pointed Hopf algebras in odd characteristic introduced by Angiono, Heckenberger and the first author, proving that they satisfy the aforementioned conjecture. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_05881 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the finite generation of the cohomology of abelian extensions of Hopf algebras Andruskiewitsch, Nicolás Natale, Sonia Quantum Algebra 16T05, 17B37, 18M05 A finite-dimensional Hopf algebra is called quasi-split if it is Morita equivalent to a split abelian extension of Hopf algebras. Combining results of Schauenburg and Negron, it is shown that every quasi-split finite-dimensional Hopf algebra satisfies the finite generation cohomology conjecture of Etingof and Ostrik. This is applied to a family of pointed Hopf algebras in odd characteristic introduced by Angiono, Heckenberger and the first author, proving that they satisfy the aforementioned conjecture. |
| title | On the finite generation of the cohomology of abelian extensions of Hopf algebras |
| topic | Quantum Algebra 16T05, 17B37, 18M05 |
| url | https://arxiv.org/abs/2407.05881 |