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arXiv · 2405.03533

Comomentum sections and Poisson maps in Hamiltonian Lie algebroids

Yuji Hirota·Noriaki Ikeda
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Abstract

In a Hamiltonian Lie algebroid over a pre-symplectic manifold and over a Poisson manifold, we introduce a map corresponding to a comomentum map, called a comomentum section. We show that the comomentum section gives a Lie algebroid morphism among Lie algebroids. Moreover, we prove that a momentum section on a Hamiltonian Lie algebroid is a Poisson map between proper Poisson manifolds, which is a generalization that a momentum map is a Poisson map between the symplectic manifold to dual of the Lie algebra. Finally, a momentum section is reinterpreted as a Dirac morphism on Dirac structures.

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Yuji Hirota, Noriaki Ikeda. 2024-05-06. Comomentum sections and Poisson maps in Hamiltonian Lie algebroids. https://doi.org/10.3842/sigma.2025.003

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