Comomentum sections and Poisson maps in Hamiltonian Lie algebroids

Abstract

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 section on a Hamiltonian Lie algebroid is a Poisson map between proper Poisson manifolds, which is a generalization that a momentum map is a Poisson map between the symplectic manifold to dual of the Lie algebra. Finally, a momentum section is reinterpreted as a Dirac morphism on Dirac structures.

21 pages. arXiv admin note: text overlap with arXiv:2309.10996

References in corpus (5)

• AKSZ-BV Formalism and Courant Algebroid-induced Topological Field Theories
• Momentum section on Courant algebroid and constrained Hamiltonian mechanics
• Homotopy momentum sections on multisymplectic manifolds
• Hamiltonian Lie algebroids over Poisson manifolds
• Hamilton Lie algebroids over Dirac structures and sigma models