Structures de tressage du groupe de Poisson formel dual d'une bigèbre de Lie quasitriangulaire

Details Structures de tressage du groupe de Poisson formel dual d'une bigèbre de Lie quasitriangulaire Structures de tressage du groupe de Poisson formel dual d'une bigèbre de Lie quasitriangulaire

1998-03-23

arxiv.org/abs/math/9803104v1

J. Pure Appl. Algebra 161 (2001), no. 3, 295-307

Mathematics

Quantum Algebra

AMS-TeX file, 12 pages

Scientific paper

Let g be a quasitriangular Lie bialgebra over a field K of characteristic zero, and let g^* be its dual Lie bialgebra. We prove that the formal Poisson group K[[g^*]] is a braided Hopf algebra, thus generalizing a result due to Reshetikhin (in the case g = sl(2,K)). The proof is via quantum groups, using the existence of a quasitriangular quantization of g^*, as well as the fact that this one provides also a quantization of K[[g^*]].

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