Reduction of Poisson manifolds with Hamiltonian Lie algebroids
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866908539038990336 |
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| author | Hirota, Yuji Ikeda, Noriaki |
| author_facet | Hirota, Yuji Ikeda, Noriaki |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_10969 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Reduction of Poisson manifolds with Hamiltonian Lie algebroids Hirota, Yuji Ikeda, Noriaki Symplectic Geometry Differential Geometry 53D20 (Primary) 53D17, 70G45 (Secondary) 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. |
| title | Reduction of Poisson manifolds with Hamiltonian Lie algebroids |
| topic | Symplectic Geometry Differential Geometry 53D20 (Primary) 53D17, 70G45 (Secondary) |
| url | https://arxiv.org/abs/2411.10969 |