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arXiv · 2506.16292

Failure of flatness over finite-dimensional Hopf subalgebras

Serge Skryabin
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Abstract

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.

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Serge Skryabin. 2025-06-19. Failure of flatness over finite-dimensional Hopf subalgebras. https://arxiv.org/abs/2506.16292

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