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arXiv · 1505.04612

Classification of four dimensional real Lie bialgebras of symplectic type and their Poisson-Lie groups

J. Abedi-Fardad·A. Rezaei-Aghdam·Gh. Haghighatdoost
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Abstract

In this paper we classify all four dimensional real Lie bialgebras of symplectic type. The classical r- matrices for these Lie bialgebras and Poisson structures on all of the related four dimensional Poisson-Lie groups are also obtained. Some new integrable models for which the Poisson-Lie group plays the role as a phase space and its dual Lie group plays the role of a symmetry group of the system, are obtained.

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J. Abedi-Fardad, A. Rezaei-Aghdam, Gh. Haghighatdoost. 2015-05-18. Classification of four dimensional real Lie bialgebras of symplectic type and their Poisson-Lie groups. https://doi.org/10.1134/s0040577917010019

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