Failure of flatness over finite-dimensional Hopf subalgebras
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909653849341952 |
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| author | Skryabin, Serge |
| author_facet | Skryabin, Serge |
| contents | It is proved in this paper that for any finite-dimensional nonsemisimple Hopf algebra $A$ there exists a Hopf algebra $H$ containing $A$ as a Hopf subalgebra such that $H$ is not flat over $A$. On the other hand, there is a class of infinite-dimensional Hopf algebras with the property that all Hopf algebras without exception are faithfully flat modules over Hopf subalgebras from this class. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_16292 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Failure of flatness over finite-dimensional Hopf subalgebras Skryabin, Serge Rings and Algebras It is proved in this paper that for any finite-dimensional nonsemisimple Hopf algebra $A$ there exists a Hopf algebra $H$ containing $A$ as a Hopf subalgebra such that $H$ is not flat over $A$. On the other hand, there is a class of infinite-dimensional Hopf algebras with the property that all Hopf algebras without exception are faithfully flat modules over Hopf subalgebras from this class. |
| title | Failure of flatness over finite-dimensional Hopf subalgebras |
| topic | Rings and Algebras |
| url | https://arxiv.org/abs/2506.16292 |