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Volume 24, Issue 2, March 2017, Pages 149 - 170
Some compatible Poisson structures and integrable bi-Hamiltonian systems on four dimensional and nilpotent six dimensional symplectic real Lie groups
Authors
Jafar Abedi-Fardad
Department of Mathematics, University of Bonab, Tabriz, Iran,j.abedifardad@bonabu.ac.ir
Adel Rezaei-Aghdam
Department of Physics, Azarbaijan Shahid Madani University, 53714-161, Tabriz, Iran,rezaei-a@azaruniv.edu
Ghorbanali Haghighatdoost
Department of Mathematics, Azarbaijan Shahid Madani University, 53714-161, Tabriz, Iran,gorbanali@azaruniv.edu
Received 22 October 2016, Accepted 18 January 2017, Available Online 6 January 2021.
- DOI
- 10.1080/14029251.2017.1306944How to use a DOI?
- Keywords
- Integrable bi-Hamiltonian system; Compatible Poisson structures; Symplectic Lie group
- Abstract
We provide an alternative method for obtaining of compatible Poisson structures on Lie groups by means of the adjoint representations of Lie algebras. In this way we calculate some compatible Poisson structures on four dimensional and nilpotent six dimensional symplectic real Lie groups. Then using Magri-Morosi’s theorem we obtain new bi-Hamiltonian systems with four dimensional and nilpotent six dimensional symplectic real Lie groups as phase spaces.
- Copyright
- © 2017 The Authors. Published by Atlantis Press and Taylor & Francis
- Open Access
- This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).
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Cite this article
TY - JOUR AU - Jafar Abedi-Fardad AU - Adel Rezaei-Aghdam AU - Ghorbanali Haghighatdoost PY - 2021 DA - 2021/01/06 TI - Some compatible Poisson structures and integrable bi-Hamiltonian systems on four dimensional and nilpotent six dimensional symplectic real Lie groups JO - Journal of Nonlinear Mathematical Physics SP - 149 EP - 170 VL - 24 IS - 2 SN - 1776-0852 UR - https://doi.org/10.1080/14029251.2017.1306944 DO - 10.1080/14029251.2017.1306944 ID - Abedi-Fardad2021 ER -