AbstractQuasitriangular Hopf algebras are Hopf algebras whose finite-dimensional representations form braided rigid tensor categories, which are naturally related thto low-dimensional topology. Drinfel'd introudced quasitriangular Hopf algebras to give solutions to the quantum Yang-Baxter equations. Given an arbitrary Hopf algebra, it’s difficult to give all possible quasitriangular structures...
AbstractA modular tensor category is a non-degenerate ribbon finite tensor category. We will constructribbon factorizable Hopfalgebras whose representation categories are modular tensor categories.Specifically, we give some general constructionmethods of ribbon factorizable Honf algebras. Thenwe use these methods to obtain a family of semisimple ribborfactorizable Hopf algebras and twofamilies ...
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