Fusion rings arising from normal Hopf subalgebras

TL;DR

This paper characterizes the fusion rings derived from normal commutative Hopf subalgebras within semisimple Hopf algebras, providing explicit descriptions especially for cyclic groups of prime order and their powers.

Contribution

It offers a detailed description of the restriction rings of modules in semisimple Hopf algebras with normal commutative subalgebras, including explicit fusion ring classifications for certain cyclic groups.

Findings

Complete description of fusion rings for G=Z_p

Extension of results to G=Z_{p^n}

Applications to understanding Hopf algebra module restrictions

Abstract

For any normal commutative Hopf subalgebra $K=k^G$ of a semisimple Hopf algebra we describe the ring inside $kG$ obtained by the restriction of $H$-modules. If $G=\Z_p$ this ring determines a fusion ring and we give a complete description for it. The case $G=\Z_{p^n}$ and some other applications are presented.