The Double and Dual of a Quasitriangular Lie Bialgebra

Details The Double and Dual of a Quasitriangular Lie Bialgebra The Double and Dual of a Quasitriangular Lie Bialgebra

2000-08-11

arxiv.org/abs/math/0008086v2

Mathematics

Quantum Algebra

LaTeX2e, 14 pages. Revised version contains new Section 6

Scientific paper

Let G be a connected, simply connected Poisson-Lie group with quasitriangular Lie bialgebra g. An explicit description of the double D(g) is given, together with the embeddings of g and g^*. This description is then used to provide a construction of the double D(G). The aim of this work is to describe D(G) in sufficient detail to be able to apply the procedures of Semenov-Tian-Shansky and Drinfeld for the classification of symplectic leaves and Poisson homogeneous spaces for Poisson-Lie groups.

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