Geodesic
Classification of four-dimensional real Lie bialgebras of symplectic type and their Poisson--Lie groups
Teoretičeskaâ i matematičeskaâ fizika, Tome 190 (2017) no. 1, pp. 3-20

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We classify all four-dimensional real Lie bialgebras of symplectic type and obtain the classical $r$-matrices for these Lie bialgebras and Poisson structures on all the associated four-dimensional Poisson–Lie groups. We obtain some new integrable models where a Poisson–Lie group plays the role of the phase space and its dual Lie group plays the role of the symmetry group of the system.
Keywords: Lie bialgebra, classical $r$-matrix, integrable system.
Mots-clés : Poisson–Lie group 
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     author = {J. Abedi-Fardad and A. Rezaei-Aghdam and Gh. Haghighatdoost},
     title = {Classification of four-dimensional real {Lie} bialgebras of symplectic type and their {Poisson--Lie} groups},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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     number = {1},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2017_190_1_a0/}
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J. Abedi-Fardad; A. Rezaei-Aghdam; Gh. Haghighatdoost. Classification of four-dimensional real Lie bialgebras of symplectic type and their Poisson--Lie groups. Teoretičeskaâ i matematičeskaâ fizika, Tome 190 (2017) no. 1, pp. 3-20. http://geodesic.mathdoc.fr/item/TMF_2017_190_1_a0/