Coquasitriangular structures on Hopf algebras constructed via abelian extensions

Abstract

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

We wish to note that Proposition 5.1 and Corollary 5.2 contained errors in the previous version. These have been corrected in the current manuscript.All comments are welcome!