Structure of semisimple Hopf algebras of dimension $p^2{q}^2$

Abstract

Let $p,q$ be prime numbers with $p^4<q$, and $k$ an algebraically closed field of characteristic 0. We show that semisimple Hopf algebras of dimension $p^2{q}^2$ can be constructed either from group algebras and their duals by means of extensions, or from Radford biproduct $R#kG$, where $kG$ is the group algebra of group $G$ of order $p^2$, $R$ is a semisimple Yetter-Drinfeld Hopf algebra in ${}_{kG}^{kG}\mathcal{YD}$ of dimension $q^2$. As an application, the special case that the structure of semisimple Hopf algebras of dimension $4q^2$ is given.

arXiv comment11pages, to appear in Communications in Algebra

Cited by in corpus (2)

• Semisimple Hopf algebras of dimension $2q^3$
• Structure theorems for semisimple Hopf algebras of dimension $p{q}^3$