Comomentum Sections and Poisson Maps in Hamiltonian Lie Algebroids
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...
Saved in:
| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Date: | 2025 |
| ISSN: | 1815-0659 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Інститут математики НАН України
2025
|
| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/212888 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| 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 |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Summary: | 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.
|
|---|---|
| ISSN: | 1815-0659 |