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This article is cited in 2 scientific papers (total in 2 papers)
Classification of four-dimensional real Lie bialgebras of symplectic type and their Poisson–Lie groups
J. Abedi-Fardadab, A. Rezaei-Aghdama, Gh. Haghighatdoostcb
a Department of Physics, Azarbaijan Shahid Madani University, Tabriz, Iran
b Department of Mathematics, University of Bonab, Tabriz, Iran
c Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran
Abstract:
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, Poisson–Lie group, classical $r$-matrix, integrable system
DOI:
https://doi.org/10.4213/tmf9020
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Theoretical and Mathematical Physics, 2017, 190:1, 1–17
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Received: 04.08.2015
Revised: 21.12.2015
Citation:
J. Abedi-Fardad, A. Rezaei-Aghdam, Gh. Haghighatdoost, “Classification of four-dimensional real Lie bialgebras of symplectic type and their Poisson–Lie groups”, TMF, 190:1 (2017), 3–20; Theoret. and Math. Phys., 190:1 (2017), 1–17
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http://mi.mathnet.ru/eng/tmf9020https://doi.org/10.4213/tmf9020 http://mi.mathnet.ru/eng/tmf/v190/i1/p3
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This publication is cited in the following articles:
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Abedi-Fardad J., Rezaei-Aghdam A., Haghighatdoost G., “Some Compatible Poisson Structures and Integrable Bi-Hamiltonian Systems on Four Dimensional and Nilpotent Six Dimensional Symplectic Real Lie Groups”, J. Nonlinear Math. Phys., 24:2 (2017), 149–170
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Z. Ravanpak, A. Rezaei-Aghdam, G. Haghighatdoost, “Invariant Poisson–Nijenhuis structures on Lie groups and classification”, Int. J. Geom. Methods Mod. Phys., 15:4 (2018), 1850059
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