# Frobenius Divisibility and Hopf Centers

## TL;DR

This paper explores divisibility properties of irreducible representations in Hopf algebras, extending classical group theory results to a broader algebraic context.

## Contribution

It generalizes Schur's divisibility theorem from finite groups to specific classes of Hopf algebras, revealing new structural insights.

## Key findings

- Divisibility results for irreducible representations of Hopf algebras
- Extension of classical group theory theorems to Hopf algebra context
- Identification of conditions under which divisibility holds

## Abstract

A classical theorem of I. Schur states that the degree of any irreducible complex representation of a finite group $G$ divides the order of $G/\mathscr{Z} G$, where $\mathscr{Z} G$ is the center $G$. This note discusses similar divisibility results for certain classes of Hopf algebras.