Classification of real three-dimensional Lie bialgebras and their Poisson-Lie groups

被引：21

作者：

Rezaei-Aghdam, A ^{[1
]}

Hemmati, M ^{[1
]}

Rastkar, AR ^{[1
]}

机构：

[1] Azarbaijan Univ Tarbiat Moallem, Dept Phys, Tabriz 53714161, Iran

来源：

JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL | 2005年 / 38卷 / 18期

关键词：

D O I：

10.1088/0305-4470/38/18/008

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

Classical r-matrices of the three-dimensional real Lie bialgebras are obtained. In this way, all three-dimensional real coboundary Lie bialgebras and their types (triangular, quasitriangular or factorizable) are classified. Then, by using the Sklyanin bracket, the Poisson structures on the related Poisson-Lie groups are obtained.

引用

页码：3981 / 3994

页数：14

共 50 条

[41] Isometry groups of three-dimensional Lie groups
Ana Cosgaya
Silvio Reggiani
Annals of Global Analysis and Geometry, 2022, 61 : 831 - 845
[42] Surfaces in three-dimensional Lie groups
Berdinsky, DA
Taimanov, IA
SIBERIAN MATHEMATICAL JOURNAL, 2005, 46 (06) : 1005 - 1019
[43] Surfaces in Three-Dimensional Lie Groups
D. A. Berdinsky
I. A. Taimanov
Siberian Mathematical Journal, 2005, 46 : 1005 - 1019
[44] Symplectic leaves of complex reductive Poisson-Lie groups
Yakimov, M
DUKE MATHEMATICAL JOURNAL, 2002, 112 (03) : 453 - 509
[45] Classification of real low-dimensional Jacobi (generalized)-Lie bialgebras
Rezaei-Aghdam, A.
Sephid, M.
INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS, 2017, 14 (01)
[46] LIE BIALGEBRAS ARISING FROM POISSON BIALGEBRAS
Oh, Sei-Qwon
Cho, Eun-Hee
JOURNAL OF THE KOREAN MATHEMATICAL SOCIETY, 2010, 47 (04) : 705 - 718
[47] Graded Poisson-Lie structures on general linear groups
Arutyunov, GE
Medvedev, PB
THEORETICAL AND MATHEMATICAL PHYSICS, 1996, 108 (01) : 916 - 929
[48] POISSON-LIE GROUPS AND CLASSICAL W-ALGEBRAS
FATEEV, VA
LUKYANOV, SL
INTERNATIONAL JOURNAL OF MODERN PHYSICS A, 1992, 7 (05): : 853 - 876
[49] Classification of all Poisson-Lie structures on an infinite-dimensional jet group
Kupershmidt, BA
Stoyanov, OS
LETTERS IN MATHEMATICAL PHYSICS, 1996, 37 (01) : 1 - 9
[50] Jacobi structures on real two- and three-dimensional Lie groups and their Jacobi–Lie systems
H. Amirzadeh-Fard
G. Haghighatdoost
P. Kheradmandynia
A. Rezaei-Aghdam
Theoretical and Mathematical Physics, 2020, 205 : 1393 - 1410

← 1 2 3 4 5 →