Geodesic
Compatible $E$-Differential Forms on Lie Algebroids over (Pre-)Multisymplectic Manifolds
Symmetry, integrability and geometry: methods and applications, Tome 20 (2024) Cet article a éte moissonné depuis la source Math-Net.Ru

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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.
Keywords: Poisson geometry, multisymplectic geometry, higher structures.
Mots-clés : Lie algebroid 
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     author = {Noriaki Ikeda},
     title = {Compatible $E${-Differential} {Forms} on {Lie} {Algebroids} over {(Pre-)Multisymplectic} {Manifolds}},
     journal = {Symmetry, integrability and geometry: methods and applications},
     year = {2024},
     volume = {20},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2024_20_a24/}
}
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Noriaki Ikeda. Compatible $E$-Differential Forms on Lie Algebroids over (Pre-)Multisymplectic Manifolds. Symmetry, integrability and geometry: methods and applications, Tome 20 (2024). http://geodesic.mathdoc.fr/item/SIGMA_2024_20_a24/

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