math-ph

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# Title: Exchanging the phase space and symmetry group of integrable Hamiltonian systems related to Lie bialgebra of bi-symplectic type

Abstract: We construct integrable Hamiltonian systems with Lie bialgebra of bi-symplectic type for which the Poisson-Lie group $G$ plays the role of phase space and its dual Lie group $\tilde{G}$ plays the role of symmetry group of the system. We give the new transformation to exchange the role of phase space and symmetry group. We obtain relation between integrals of motion of these two integrable systems. Finally we give some examples about real four dimensional Lie bialgebras of bi-symplectic type.
 Comments: 10 pages Subjects: Mathematical Physics (math-ph) Cite as: arXiv:1803.06886 [math-ph] (or arXiv:1803.06886v1 [math-ph] for this version)