Comomentum Sections and Poisson Maps in Hamiltonian Lie Algebroids
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 se...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2025 |
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2025
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/212888 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Comomentum Sections and Poisson Maps in Hamiltonian Lie Algebroids. Yuji Hirota and Noriaki Ikeda. SIGMA 21 (2025), 003, 21 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862728645738496000 |
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| author | Hirota, Yuji Ikeda, Noriaki |
| author_facet | Hirota, Yuji Ikeda, Noriaki |
| citation_txt | Comomentum Sections and Poisson Maps in Hamiltonian Lie Algebroids. Yuji Hirota and Noriaki Ikeda. SIGMA 21 (2025), 003, 21 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | 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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| first_indexed | 2026-03-21T17:45:45Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-212888 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-21T17:45:45Z |
| publishDate | 2025 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Hirota, Yuji Ikeda, Noriaki 2026-02-13T13:51:07Z 2025 Comomentum Sections and Poisson Maps in Hamiltonian Lie Algebroids. Yuji Hirota and Noriaki Ikeda. SIGMA 21 (2025), 003, 21 pages 1815-0659 2020 Mathematics Subject Classification: 53D17; 53D20; 53D05 arXiv:2405.03533 https://nasplib.isofts.kiev.ua/handle/123456789/212888 https://doi.org/10.3842/SIGMA.2025.003 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. The authors would like to thank Antonio Miti and the referees for their useful discussion and comments. Especially, they would like to thank the anonymous referees for their relevant contributions to improve the paper. This work was supported by JSPS Grants-in-Aid for Scientific Research Number 22K03323. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Comomentum Sections and Poisson Maps in Hamiltonian Lie Algebroids Article published earlier |
| spellingShingle | Comomentum Sections and Poisson Maps in Hamiltonian Lie Algebroids Hirota, Yuji Ikeda, Noriaki |
| title | Comomentum Sections and Poisson Maps in Hamiltonian Lie Algebroids |
| title_full | Comomentum Sections and Poisson Maps in Hamiltonian Lie Algebroids |
| title_fullStr | Comomentum Sections and Poisson Maps in Hamiltonian Lie Algebroids |
| title_full_unstemmed | Comomentum Sections and Poisson Maps in Hamiltonian Lie Algebroids |
| title_short | Comomentum Sections and Poisson Maps in Hamiltonian Lie Algebroids |
| title_sort | comomentum sections and poisson maps in hamiltonian lie algebroids |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/212888 |
| work_keys_str_mv | AT hirotayuji comomentumsectionsandpoissonmapsinhamiltonianliealgebroids AT ikedanoriaki comomentumsectionsandpoissonmapsinhamiltonianliealgebroids |