Failure of flatness over finite-dimensional Hopf subalgebras

Serge Skryabin

Failure of flatness over finite-dimensional Hopf subalgebras

Rings and Algebras 2025-06-23 v1

Authors: Serge Skryabin

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.

Keywords

Hopf algebra flatness finite-dimensional Hopf subalgebra faithfully flat module

Cite

@article{arxiv.2506.16292,
  title  = {Failure of flatness over finite-dimensional Hopf subalgebras},
  author = {Serge Skryabin},
  journal= {arXiv preprint arXiv:2506.16292},
  year   = {2025}
}