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Local quasitriangular Hopf algebras. (English) Zbl 1179.16017

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.
Reviewer: Li Fang (Hangzhou)

MSC:

16T05 Hopf algebras and their applications
18D10 Monoidal, symmetric monoidal and braided categories (MSC2010)
16T25 Yang-Baxter equations
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