On normal Hopf subalgebras of semisimple Hopf algebras

TL;DR

This paper generalizes Masuoka's criterion to identify normal Hopf subalgebras in semisimple Hopf algebras, providing new insights into their structure and character theory.

Contribution

It introduces a new criterion for subcoalgebras to be invariant under the adjoint action, extending previous results on normal Hopf subalgebras.

Findings

Generalized Masuoka's criterion for normality

Character-theoretic description of induction and restriction

Identified conditions for subcoalgebras to be invariant

Abstract

A criterion for subcoalgebras to be invariant under the adjoint action is given generalizing Masuoka's criterion for normal Hopf subalgebras. At the level of characters, the image of the induction functor from a normal Hopf subalgebra is isomorphic to the image of the restriction functor.