English

Some compatible Poisson structures and integrable bi-Hamiltonian systems on four dimensional and nilpotent six dimensional symplectic real Lie groups

Symplectic Geometry 2017-04-06 v2 Mathematical Physics Differential Geometry math.MP

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.

Keywords

Cite

@article{arxiv.1610.09931,
  title  = {Some compatible Poisson structures and integrable bi-Hamiltonian systems on four dimensional and nilpotent six dimensional symplectic real Lie groups},
  author = {J. Abedi-Fardad and A. Rezaei-Aghdam and Gh. Haghighatdoost},
  journal= {arXiv preprint arXiv:1610.09931},
  year   = {2017}
}

Comments

19 pages, 4 table