Monoidal invariance of the cohomological dimension of Hopf algebras: the finite case
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866912902616711168 |
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| author | Bichon, Julien |
| author_facet | Bichon, Julien |
| contents | A consequence of the recent work of Ren and Zhu on Gorenstein projective dimensions of modules over Hopf algebras is that if $A$ and $B$ are Hopf algebras with bijective antipodes having equivalent linear tensor categories of comodules and both having finite global dimensions, then their global dimensions coincide. In this note we provide a direct proof of this result, without using Gorenstein projective dimensions, and we notice that the assumption on the bijectivity of the antipodes can be removed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_12731 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Monoidal invariance of the cohomological dimension of Hopf algebras: the finite case Bichon, Julien K-Theory and Homology Quantum Algebra Rings and Algebras A consequence of the recent work of Ren and Zhu on Gorenstein projective dimensions of modules over Hopf algebras is that if $A$ and $B$ are Hopf algebras with bijective antipodes having equivalent linear tensor categories of comodules and both having finite global dimensions, then their global dimensions coincide. In this note we provide a direct proof of this result, without using Gorenstein projective dimensions, and we notice that the assumption on the bijectivity of the antipodes can be removed. |
| title | Monoidal invariance of the cohomological dimension of Hopf algebras: the finite case |
| topic | K-Theory and Homology Quantum Algebra Rings and Algebras |
| url | https://arxiv.org/abs/2602.12731 |