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.

中文翻译：

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每个辛流形都是一个（线性）共伴轨道

我们证明，对于任何辛形式的周期群，每个辛流形都是其积分丛的自同构群的共伴轨道，线性作用于其动量空间。当辛流形在李群的作用下是齐次的并且辛形式是积分时，这个结果推广了 Kirilov-Kostant-Souriau 定理。