Some compatible Poisson structures and integrable bi-Hamiltonian systems   on four dimensional and nilpotent six dimensional symplectic real Lie groups
  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. 
J. Abedi-Fardad, A. Rezaei-Aghdam, Gh. Haghighatdoost
math.SG math-ph math.DG math.MP