CLASSIFICATION OF FOUR-DIMENSIONAL REAL LIE BIALGEBRAS OF SYMPLECTIC TYPE AND THEIR POISSON-LIE GROUPS

被引：7

作者：

Abedi-Fardad, J. ^{[1
,2
]}

Rezaei-Aghdam, A. ^{[2
]}

Haghighatdoost, Gh. ^{[1
,3
]}

机构：

[1] Univ Bonab, Dept Math, Tabriz, Iran

[2] Azarbaijan Shahid Madani Univ, Dept Phys, Tabriz, Iran

[3] Azarbaijan Shahid Madani Univ, Dept Math, Tabriz, Iran

来源：

THEORETICAL AND MATHEMATICAL PHYSICS | 2017年 / 190卷 / 01期

关键词：

Lie bialgebra; Poisson-Lie group; classical r-matrix; integrable system; ALGEBRAS;

D O I：

10.1134/S0040577917010019

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

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.

引用

页码：1 / 17

页数：17

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