Zhang, Shouchuan; Gould, Mark D.; Zhang, Yao-Zhong Local quasitriangular Hopf algebras. (English) Zbl 1179.16017 SIGMA, Symmetry Integrability Geom. Methods Appl. 4, Paper 042, 14 p. (2008). 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 Keywords:local quasitriangular Hopf algebras; Yang-Baxter equation; braided tensor categories PDFBibTeX XMLCite \textit{S. Zhang} et al., SIGMA, Symmetry Integrability Geom. Methods Appl. 4, Paper 042, 14 p. (2008; Zbl 1179.16017) Full Text: DOI arXiv EuDML