Compatible -Differential Forms on Lie Algebroids over (Pre-)Multisymplectic Manifolds
We consider higher generalizations of both a (twisted) Poisson structure and the equivariant condition of a momentum map on a symplectic manifold. On a Lie algebroid over a (pre-)symplectic and (pre-)multisymplectic manifold, we introduce a Lie algebroid differential form called a compatible --form....
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2024 |
| Автор: | |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2024
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/212170 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Compatible -Differential Forms on Lie Algebroids over (Pre-)Multisymplectic Manifolds. Noriaki Ikeda. SIGMA 20 (2024), 025, 19 pages |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862750823551860736 |
|---|---|
| author | Ikeda, Noriaki |
| author_facet | Ikeda, Noriaki |
| citation_txt | Compatible -Differential Forms on Lie Algebroids over (Pre-)Multisymplectic Manifolds. Noriaki Ikeda. SIGMA 20 (2024), 025, 19 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We consider higher generalizations of both a (twisted) Poisson structure and the equivariant condition of a momentum map on a symplectic manifold. On a Lie algebroid over a (pre-)symplectic and (pre-)multisymplectic manifold, we introduce a Lie algebroid differential form called a compatible --form. This differential form satisfies a compatibility condition, which is consistent with both the Lie algebroid structure and the (pre-)(multi)symplectic structure. There are many interesting examples, such as a Poisson structure, a twisted Poisson structure, and a twisted -Poisson structure for a pre--plectic manifold. Moreover, momentum maps and momentum sections on symplectic manifolds, homotopy momentum maps and homotopy momentum sections on multisymplectic manifolds have this structure.
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| first_indexed | 2026-03-21T18:11:20Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-212170 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-21T18:11:20Z |
| publishDate | 2024 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Ikeda, Noriaki 2026-01-30T08:17:34Z 2024 Compatible -Differential Forms on Lie Algebroids over (Pre-)Multisymplectic Manifolds. Noriaki Ikeda. SIGMA 20 (2024), 025, 19 pages 1815-0659 2020 Mathematics Subject Classification: 53D17; 53D20; 58A50 arXiv:2302.08193 https://nasplib.isofts.kiev.ua/handle/123456789/212170 https://doi.org/10.3842/SIGMA.2024.025 We consider higher generalizations of both a (twisted) Poisson structure and the equivariant condition of a momentum map on a symplectic manifold. On a Lie algebroid over a (pre-)symplectic and (pre-)multisymplectic manifold, we introduce a Lie algebroid differential form called a compatible --form. This differential form satisfies a compatibility condition, which is consistent with both the Lie algebroid structure and the (pre-)(multi)symplectic structure. There are many interesting examples, such as a Poisson structure, a twisted Poisson structure, and a twisted -Poisson structure for a pre--plectic manifold. Moreover, momentum maps and momentum sections on symplectic manifolds, homotopy momentum maps and homotopy momentum sections on multisymplectic manifolds have this structure. The author is grateful to the Erwin Schr¨odinger International Institute for Mathematics and Physics for support within the program “Higher Structures and Field Theory” in 2022, and the National Center for Theoretical Sciences and National Tsing Hua University, where part of this work was carried out, for their hospitality. This work was supported by JSPS Grants-in-Aid for Scientific Research Number 22K03323. I would like to thank Hsuan-Yi Liao, Camille Laurent-Gengoux, and Seokbong Seol for their hospitality and useful discussion. Especially, he would like to thank the anonymous referees for their relevant contributions to improve the paper. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Compatible -Differential Forms on Lie Algebroids over (Pre-)Multisymplectic Manifolds Article published earlier |
| spellingShingle | Compatible -Differential Forms on Lie Algebroids over (Pre-)Multisymplectic Manifolds Ikeda, Noriaki |
| title | Compatible -Differential Forms on Lie Algebroids over (Pre-)Multisymplectic Manifolds |
| title_full | Compatible -Differential Forms on Lie Algebroids over (Pre-)Multisymplectic Manifolds |
| title_fullStr | Compatible -Differential Forms on Lie Algebroids over (Pre-)Multisymplectic Manifolds |
| title_full_unstemmed | Compatible -Differential Forms on Lie Algebroids over (Pre-)Multisymplectic Manifolds |
| title_short | Compatible -Differential Forms on Lie Algebroids over (Pre-)Multisymplectic Manifolds |
| title_sort | compatible -differential forms on lie algebroids over (pre-)multisymplectic manifolds |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/212170 |
| work_keys_str_mv | AT ikedanoriaki compatibledifferentialformsonliealgebroidsoverpremultisymplecticmanifolds |