The Double and Dual of a Quasitriangular Lie Bialgebra
Quantum Algebra
2007-05-23 v2
Abstract
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.
Keywords
Cite
@article{arxiv.math/0008086,
title = {The Double and Dual of a Quasitriangular Lie Bialgebra},
author = {Timothy J. Hodges and Milen Yakimov},
journal= {arXiv preprint arXiv:math/0008086},
year = {2007}
}
Comments
LaTeX2e, 14 pages. Revised version contains new Section 6