Journal of Nonlinear Mathematical Physics

In Press, Corrected Proof, Available Online: 17 December 2020

Compatible Poisson Structures and bi-Hamiltonian Systems Related to Low-dimensional Lie Algebras

Authors
Gh. Haghighatdoost1, *, S. Abdolhadi-Zangakani2, J. Abedi-Fardad1
1Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz 53714-161, Iran
2Department of Mathematics, University of Bonab, Tabriz, Iran
*Corresponding author. Email: gorbanali@azaruniv.ac.ir
Corresponding Author
Gh. Haghighatdoost
Received 29 June 2020, Accepted 31 October 2020, Available Online 17 December 2020.
DOI
https://doi.org/10.2991/jnmp.k.201104.001How to use a DOI?
Keywords
Compatible Poisson structures, bi-Hamiltonian system, Lie groups
Abstract

In this work, we give a method to construct compatible Poisson structures on Lie groups by means of structure constants of their Lie algebras and some vector field. In this way we calculate some compatible Poisson structures on low-dimensional Lie groups. Then, using a theorem by Magri and Morosi, we obtain new integrable bi-Hamiltonian systems with two-, four- and six-dimensional symplectic real Lie groups as phase spaces.

Copyright
© 2020 The Authors. Published by Atlantis Press B.V.
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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Journal
Journal of Nonlinear Mathematical Physics
Publication Date
2020/12
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
https://doi.org/10.2991/jnmp.k.201104.001How to use a DOI?
Copyright
© 2020 The Authors. Published by Atlantis Press B.V.
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/).

Cite this article

TY  - JOUR
AU  - Gh. Haghighatdoost
AU  - S. Abdolhadi-Zangakani
AU  - J. Abedi-Fardad
PY  - 2020
DA  - 2020/12
TI  - Compatible Poisson Structures and bi-Hamiltonian Systems Related to Low-dimensional Lie Algebras
JO  - Journal of Nonlinear Mathematical Physics
SN  - 1776-0852
UR  - https://doi.org/10.2991/jnmp.k.201104.001
DO  - https://doi.org/10.2991/jnmp.k.201104.001
ID  - Haghighatdoost2020
ER  -