Homogeneous symplectic manifolds of Poisson-Lie groups
Symplectic Geometry
2007-05-23 v1 Differential Geometry
Abstract
Symplectic manifolds which are homogeneous spaces of Poisson-Lie groups are studied in this paper. We show that these spaces are, under certain assumptions, covering spaces of dressing orbits of the Poisson-Lie groups which act on them. The effect of the Poisson induction procedure on such spaces is also examined, thus leading to an interesting generalization of the notion of homogeneous space. Some examples of homogeneous spaces of Poisson-Lie groups are discussed in the light of the previous results.
Keywords
Cite
@article{arxiv.math/0101139,
title = {Homogeneous symplectic manifolds of Poisson-Lie groups},
author = {Pierre Baguis},
journal= {arXiv preprint arXiv:math/0101139},
year = {2007}
}
Comments
15 pages, Plain TeX