Hopf algebraic homogeneous spaces interpreted rationally: the Abe-Kanno theorem

Serge Skryabin

Hopf algebraic homogeneous spaces interpreted rationally: the Abe-Kanno theorem

Rings and Algebras 2026-07-01 v1

Authors: Serge Skryabin

Abstract

We present a Hopf algebraic generalization of the Abe-Kanno theorem on a correspondence between subgroups of an algebraic group and invariant subfields of the field of rational functions. It applies to residually finite-dimensional Hopf algebras admitting an artinian classical quotient ring and is used in the paper to derive some general properties of such Hopf algebras.

Keywords

Hopf algebras homogeneous spaces Abe-Kanno theorem invariant subfields residually finite-dimensional

Cite

@article{arxiv.2607.01195,
  title  = {Hopf algebraic homogeneous spaces interpreted rationally: the Abe-Kanno theorem},
  author = {Serge Skryabin},
  journal= {arXiv preprint arXiv:2607.01195},
  year   = {2026}
}

Comments

plain tex, 78 pages