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Every symplectic manifold is a (linear) coadjoint orbit
Published online by Cambridge University Press: 18 May 2021
Abstract
We prove that every symplectic manifold is a coadjoint orbit of the group of automorphisms of its integration bundle, acting linearly on its space of momenta, for any group of periods of the symplectic form. This result generalizes the Kirilov–Kostant–Souriau theorem when the symplectic manifold is homogeneous under the action of a Lie group and the symplectic form is integral.
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- © Canadian Mathematical Society 2021
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