Comomentum Sections and Poisson Maps in Hamiltonian Lie Algebroids

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2025
• Main Authors: Hirota, Yuji, Ikeda, Noriaki
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2025
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/212888
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Comomentum Sections and Poisson Maps in Hamiltonian Lie Algebroids. Yuji Hirota and Noriaki Ikeda. SIGMA 21 (2025), 003, 21 pages

In a Hamiltonian Lie algebroid over a pre-symplectic manifold and over a Poisson manifold, we introduce a map corresponding to a comomentum map, called a comomentum section. We show that the comomentum section gives a Lie algebroid morphism among Lie algebroids. Moreover, we prove that a momentum se...