Shouchuan Zhang, Mark D. Gould, Yao-Zhong Zhang, “Local Quasitriangular Hopf Algebras”, SIGMA, 2008, Volume 4,042, 14 pp.

Local Quasitriangular Hopf Algebras

Shouchuan Zhang^ab, Mark D. Gould^a, Yao-Zhong Zhang^a

^a Department of Mathematics, University of Queensland, Brisbane 4072, Australia
^b Department of Mathematics, Hunan University, Changsha 410082, P. R. China

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.

Keywords: Hopf algebra; braided category.

MSC: 16W30; 16G10

Received: January 31, 2008; in final form April 30, 2008; Published online May 9, 2008

Language: English

DOI: 10.3842/SIGMA.2008.042