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arXiv · 1009.3541

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

Jingcheng Dong
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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 $p^2q^2$ 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.

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Jingcheng Dong. 2010-11-21. Structure of semisimple Hopf algebras of dimension $p^2q^2$. https://doi.org/10.1080/00927872.2010.538458

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