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arXiv · 2411.10969

Reduction of Poisson manifolds with Hamiltonian Lie algebroids

Yuji Hirota·Noriaki Ikeda
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Abstract

Reduction theorem for Poisson manifolds with Hamiltonian Lie algebroids is presented. The notion of compatibility of a momentum section is introduced to the category of Hamiltonian Lie algebroids over Poisson manifolds. It is shown that a compatible momentum section is a Lie algebra homomorphism, and then the quotient space of the zero level set of a compatible momentum section proves to be a Poisson manifold.

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Yuji Hirota, Noriaki Ikeda. 2024-11-17. Reduction of Poisson manifolds with Hamiltonian Lie algebroids. https://arxiv.org/abs/2411.10969

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