Depth Two Hopf Subalgebras of Semisimple Hopf algebras

TL;DR

This paper proves that in finite-dimensional semisimple Hopf algebras over an algebraically closed field of characteristic zero, a Hopf subalgebra is depth two if and only if it is normal, providing a concise proof of this equivalence.

Contribution

The paper offers a short proof establishing the equivalence between depth two and normality of Hopf subalgebras in semisimple Hopf algebras.

Findings

Depth two Hopf subalgebras are exactly the normal Hopf subalgebras.

Provides a concise proof of the equivalence.

Clarifies the structure of subalgebras in semisimple Hopf algebras.

Abstract

Let H be a finite dimensional semisimple Hopf algebra over an algebraically closed field of characteristic zero. In this note we give a short proof of the fact that a Hopf subalgebra of H is a depth two subalgebra if and only if it is normal Hopf subalgebra.