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Mathematics > Differential Geometry
Title: Compatible $E$-Differential Forms on Lie Algebroids over (Pre-)Multisymplectic Manifolds
(Submitted on 16 Feb 2023 (v1), last revised 31 Mar 2024 (this version, v4))
Abstract: 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.
Submission history
From: Noriaki Ikeda [view email] [via JOURNAL proxy][v1] Thu, 16 Feb 2023 10:18:03 GMT (31kb)
[v2] Sun, 12 Nov 2023 07:52:50 GMT (29kb)
[v3] Wed, 27 Mar 2024 03:29:51 GMT (31kb)
[v4] Sun, 31 Mar 2024 10:04:00 GMT (25kb,D)
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