Local quasitriangular Hopf algebras. (Q935731)

The Yang-Baxter equation has been an important thesis in mathematics and physics. Attempts to find solutions of the Yang-Baxter equation have led to the theory of quantum groups and quasitriangular Hopf algebras. In the present paper, the authors introduce a new class of Hopf algebras, that is, local quasitriangular Hopf algebras, which generalize quasitriangular Hopf algebras. The category of modules with finite cycles over a local quasitriangular Hopf algebra is shown to be a braided tensor category, then consequently, a solution of the Yang-Baxter equation is afforded in a systematic way.