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arXiv · 2511.11254

Coquasitriangular structures on Hopf algebras constructed via abelian extensions

Jing Yu·Xiangjun Zhen
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Abstract

The aim of this paper is to study coquasitriangular structures on a class of cosemisimple Hopf algebras of the form $\Bbbk^G {}^\tau \#_{\sigma} \Bbbk F$, constructed as abelian extensions of $\Bbbk F$ by $\Bbbk^G$ for a finite group $G$ and an arbitrary group $F$. We investigate when a coquasitriangular structure exists on $\Bbbk^G{}^\tau\#_{\sigma}\Bbbk F$ and provide characterizations of its coquasitriangular structures. As an application, we study the coquasitriangular structures for the case where $G = \mathbb{Z}_2$.

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Jing Yu, Xiangjun Zhen. 2025-11-14. Coquasitriangular structures on Hopf algebras constructed via abelian extensions. https://arxiv.org/abs/2511.11254

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