by Liu, Guohua; Zhu, Shenglin

In this paper, we consider a finite dimensional semisimple cosemisimple quasitriangular Hopf algebra $(H,R\,)$ with $R^{\,21}R\in C(H\otimes H\,)$ (we call this type of Hopf algebras almost-quasitriangular) over an algebraically closed field $k$. We denote by $B$ the vector space generated by the left tensorand of $R^{\,21}R$. Then $B$ is a sub-Hopf algebra of $H$. We proved that when $\dim B$ is odd, $H$ has a triangular structure and can be obtained from a group algebra by twisting its usual comultiplication [14]; when $\dim B$ is even, $H$ is an extension of an abelian group algebra and a triangular Hopf algebra, and may not be triangular. In general, an almost-triangular Hopf algebra can be viewed as a cocycle bicrossproduct.

DOI: 10.1007/s10468-006-9021-6
Online Date: 4/27/2007
Print publication date: 12/1/2007
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