Almost-triangular Hopf Algebras |
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Authors: | Guohua Liu Shenglin Zhu |
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Institution: | (1) School of Mathematical Sciences, Fudan University, Shanghai, 200433, China;(2) Department of Mathematics, Southeast University, Nanjing, 210096, China;(3) Key Laboratory of Mathematics for Nonlinear Sciences, Fudan University, Ministry of Education, Shanghai, China |
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Abstract: | In this paper, we consider a finite dimensional semisimple cosemisimple quasitriangular Hopf algebra with (we call this type of Hopf algebras almost-quasitriangular) over an algebraically closed field . We denote by the vector space generated by the left tensorand of . Then is a sub-Hopf algebra of . We proved that when is odd, has a triangular structure and can be obtained from a group algebra by twisting its usual comultiplication 14]; when is even, 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.
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Keywords: | 16W30 |
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