Comomentum sections and Poisson maps in Hamiltonian Lie algebroids
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866912177039867904 |
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| author | Hirota, Yuji Ikeda, Noriaki |
| author_facet | Hirota, Yuji Ikeda, Noriaki |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_03533 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Comomentum sections and Poisson maps in Hamiltonian Lie algebroids Hirota, Yuji Ikeda, Noriaki Symplectic Geometry Differential Geometry 53D17, 53D20, 53D05 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. |
| title | Comomentum sections and Poisson maps in Hamiltonian Lie algebroids |
| topic | Symplectic Geometry Differential Geometry 53D17, 53D20, 53D05 |
| url | https://arxiv.org/abs/2405.03533 |