Induction of Hamiltonian Poisson actions

Details Induction of Hamiltonian Poisson actions Induction of Hamiltonian Poisson actions

2000-12-11

arxiv.org/abs/math/0012076v1

Mathematics

Symplectic Geometry

17 pages, Plain TeX file, to appear in Diff. Geom. Appl

Scientific paper

We propose a Poisson-Lie analog of the symplectic induction procedure, using an appropriate Poisson generalization of the reduction of symplectic manifolds with symmetry. Having as basic tools the equivariant momentum maps of Poisson actions, the double group of a Poisson-Lie group and the reduction of Poisson manifolds with symmetry, we show how one can induce a Poisson action admitting an equivariant momentum map. We prove that, under certain conditions, the dressing orbits of a Poisson-Lie group can be obtained by Poisson induction from the dressing orbits of a Poisson-Lie subgroup.

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