Compatible $E$-Differential Forms on Lie Algebroids over (Pre-)Multisymplectic Manifolds
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arXiv
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866914734785167360 |
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| author | Ikeda, Noriaki |
| author_facet | Ikeda, Noriaki |
| contents | 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 $E$-$n$-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 $R$-Poisson structure for a pre-$n$-plectic manifold. Moreover, momentum maps and momentum sections on symplectic manifolds, homotopy momentum maps and homotopy momentum sections on multisymplectic manifolds have this structure. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_08193 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Compatible $E$-Differential Forms on Lie Algebroids over (Pre-)Multisymplectic Manifolds Ikeda, Noriaki Differential Geometry Mathematical Physics Symplectic Geometry 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 $E$-$n$-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 $R$-Poisson structure for a pre-$n$-plectic manifold. Moreover, momentum maps and momentum sections on symplectic manifolds, homotopy momentum maps and homotopy momentum sections on multisymplectic manifolds have this structure. |
| title | Compatible $E$-Differential Forms on Lie Algebroids over (Pre-)Multisymplectic Manifolds |
| topic | Differential Geometry Mathematical Physics Symplectic Geometry |
| url | https://arxiv.org/abs/2302.08193 |