Almost-triangular hopf algebras

作者：Liu Guohua; Zhu Shenglin^*

来源：Algebras and Representation Theory, 2007, 10(6): 555-564.

DOI：10.1007/s10468-006-9021-6

• hopf algebra
• twist
• quasitriangular structure

In this paper, we consider a finite dimensional semisimple cosemisimple quasitriangular Hopf algebra (H,R) with R-21 R epsilon C(H circle times H) (we call this type of Hopf algebras almost-quasitriangular) over an algebraically closed field k. We denote by 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.

• 出版日期2007-12
• 单位复旦大学; 东南大学