Failure of flatness over finite-dimensional Hopf subalgebras

Fuente: arXiv
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Main Author: Skryabin, Serge
Format: Preprint
Published: 2025
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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