Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 4 (2008), 042, 14 pages      math.QA/0601541      https://doi.org/10.3842/SIGMA.2008.042

Local Quasitriangular Hopf Algebras

Shouchuan Zhang a, b, Mark D. Gould b and Yao-Zhong Zhang b
a) Department of Mathematics, Hunan University, Changsha 410082, P.R. China
b) Department of Mathematics, University of Queensland, Brisbane 4072, Australia

Received January 31, 2008, in final form April 30, 2008; Published online May 09, 2008

Abstract
We find a new class of Hopf algebras, local quasitriangular Hopf algebras, which generalize quasitriangular Hopf algebras. Using these Hopf algebras, we obtain solutions of the Yang-Baxter equation in a systematic way. The category of modules with finite cycles over a local quasitriangular Hopf algebra is a braided tensor category.

Key words: Hopf algebra; braided category.

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