PIERRE BAGUIS

Homogeneous symplectic manifolds of Poisson-Lie groups

Pages: 55-67
Received: 16 January 2002   
Revised: 18 March 2002
Mathematics Subject Classification (2000): 53C15 -53D17 - 53D20

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.