A note on integrabiliy of Hamiltonian systems on the co-adjoint Lie groupoids
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866910713649299456 |
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| author | Haghighatdoost, Ghorbanali Ayoubi, Rezvaneh |
| author_facet | Haghighatdoost, Ghorbanali Ayoubi, Rezvaneh |
| contents | As we said in our previous work [4], the main idea of our research is to introduce a class of Lie groupoids by means of co-adjoint representation of a Lie groupoid on its isotropy Lie algebroid, which we called coadjoint Lie groupoids. In this paper, we will examine the relationship between structural mappings of the Lie algebroid associated to Lie groupoid and co-adjoint Lie algebroid. Also, we try to construct and define integrabiliy of Hamiltonian system on the co-adjoint Lie groupoids. In addition, we show that co-adjoint Lie groupoid associated to a symplectic Lie groupoid is a symplectic Lie groupoid. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2411_16631 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A note on integrabiliy of Hamiltonian systems on the co-adjoint Lie groupoids Haghighatdoost, Ghorbanali Ayoubi, Rezvaneh Dynamical Systems Mathematical Physics 18B40, 53D17, 70H08, 37J35 As we said in our previous work [4], the main idea of our research is to introduce a class of Lie groupoids by means of co-adjoint representation of a Lie groupoid on its isotropy Lie algebroid, which we called coadjoint Lie groupoids. In this paper, we will examine the relationship between structural mappings of the Lie algebroid associated to Lie groupoid and co-adjoint Lie algebroid. Also, we try to construct and define integrabiliy of Hamiltonian system on the co-adjoint Lie groupoids. In addition, we show that co-adjoint Lie groupoid associated to a symplectic Lie groupoid is a symplectic Lie groupoid. |
| title | A note on integrabiliy of Hamiltonian systems on the co-adjoint Lie groupoids |
| topic | Dynamical Systems Mathematical Physics 18B40, 53D17, 70H08, 37J35 |
| url | https://arxiv.org/abs/2411.16631 |