Abstract

Quasitriangular 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 on it due to the lack of general methods. We will talk about the symmetry of quasitriangular structures on some Hopf algebras which can greatly simplify the problem. After that, the classification of certain quasitriangular Hopf algebras by dimension will be discussed.