Homogeneous symplectic manifolds of Poisson-Lie groups
نویسنده
چکیده
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. Key-words: Poisson-Lie groups, induction of Poisson actions, momentum mapping, homogeneous spaces MSC 2000: 53C15, 53D17, 53D20 1 e-mail: [email protected] 2 Research supported by the “Communauté française de Belgique”, through an “Action de Recherche Concertée de la Direction de la Recherche Scientifique”. 2 homogeneous symplectic manifolds of poisson-lie groups
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