Exchanging role of the phase space and symmetry group of integrable Hamiltonian systems related to Lie bialgebras of bi-symplectic types

2018/03/19 by J. Abedi-Fardad, Abedi-Fardad, J., A. Rezaei-Aghdam +3
Mathematics · Physics and Astronomy · #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.MP

paper · pdf · doi:10.48550/arxiv.1803.06886

13 pages

arxiv created 2019/02/06 · arxiv updated 2019/02/07

Abstract

We construct integrable Hamiltonian systems with Lie bialgebras (\bf g , \bf g) of the bi-symplectic type for which the Poisson-Lie groups \bf G play the role of the phase spaces, and their dual Lie groups \bf G play the role of the symmetry groups of the systems. We give the new transformations to exchange the role of phase spaces and symmetry groups and obtain the relations between integrals of motions of these integrable systems. Finally, we give some examples of real four-dimensional Lie bialgebras of bi-symplectic type.

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