Homogeneous symplectic manifolds of Poisson-Lie groups

Details Homogeneous symplectic manifolds of Poisson-Lie groups Homogeneous symplectic manifolds of Poisson-Lie groups

2001-01-17

arxiv.org/abs/math/0101139v1

Mathematics

Symplectic Geometry

15 pages, Plain TeX

Scientific paper

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.

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