Clifford theory for cocentral extensions

TL;DR

This paper extends Clifford theory to semisimple Hopf algebras, demonstrating that the classical correspondence applies to cocentral extensions, broadening the understanding of subgroup structures in algebraic systems.

Contribution

It generalizes Clifford theory to cocentral extensions in semisimple Hopf algebras, a novel extension of classical results.

Findings

Clifford correspondence holds for cocentral extensions in semisimple Hopf algebras

The paper establishes conditions under which the classical theory extends to Hopf algebra setting

Provides a framework for analyzing normal subalgebras in Hopf algebra extensions

Abstract

The classical Clifford correspondence for normal subgroups is considered in the more general setting of semisimple Hopf algebras. We prove that this correspondence still holds if the extension determined by the normal Hopf subalgebra is cocentral.