On the unicity of braidings of quasitriangular Lie bialgebras

Details On the unicity of braidings of quasitriangular Lie bialgebras On the unicity of braidings of quasitriangular Lie bialgebras

2002-07-25

arxiv.org/abs/math/0207235v1

Int. Math. Res. Not. 2003, no. 46, 2461-2486

Mathematics

Quantum Algebra

Scientific paper

Any quantization of a quasitriangular Lie bialgebra g gives rise to a braiding of the dual Poisson-Lie formal group G^*. We show that this braiding always coincides with the Weinstein-Xu braiding. We also define the lifts of the classical r-matrix r as certain functions on G^* x G^*, prove their existence and uniqueness using co-Hochschild cohomology arguments and show that the lift can be expressed in terms of r by universal formulas.

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