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....

Повний опис

Збережено в:
Бібліографічні деталі
Опубліковано в: :Symmetry, Integrability and Geometry: Methods and Applications
Дата:2024
Автор: Ikeda, Noriaki
Формат: Стаття
Мова:Англійська
Опубліковано: Інститут математики НАН України 2024
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
Опис
Резюме: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.
ISSN:1815-0659