J. Abedi-Fardad, A. Rezaei-Aghdam, Gh. Haghighatdoost, “Classification of four-dimensional real Lie bialgebras of symplectic type and their Poisson–Lie groups”, TMF, 2017, Volume 190, Number 1,Pages <nobr>3

This article is cited in 6 papers

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

J. Abedi-Fardad^ab, A. Rezaei-Aghdam^a, Gh. Haghighatdoost^cb

^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.

Received: 04.08.2015
Revised: 21.12.2015

DOI: 10.4213/tmf9020