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
收藏
页码：3981 / 3994
页数：14
相关论文
共 50 条
  • [1] Classification of real three-dimensional Poisson-Lie groups
    Ballesteros, Angel
    Blasco, Alfonso
    Musso, Fabio
    [J]. JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 2012, 45 (17)
  • [2] CLASSIFICATION OF FOUR-DIMENSIONAL REAL LIE BIALGEBRAS OF SYMPLECTIC TYPE AND THEIR POISSON-LIE GROUPS
    Abedi-Fardad, J.
    Rezaei-Aghdam, A.
    Haghighatdoost, Gh.
    [J]. THEORETICAL AND MATHEMATICAL PHYSICS, 2017, 190 (01) : 1 - 17
  • [3] CENTRAL EXTENSIONS OF LIE BIALGEBRAS AND POISSON-LIE GROUPS
    BENAYED, M
    [J]. JOURNAL OF GEOMETRY AND PHYSICS, 1995, 16 (03) : 301 - 304
  • [4] Classification of three-dimensional Lie bialgebras
    Gomez, X
    [J]. JOURNAL OF MATHEMATICAL PHYSICS, 2000, 41 (07) : 4939 - 4956
  • [5] (1+1) Schrodinger Lie bialgebras and their Poisson-Lie groups
    Ballesteros, A
    Herranz, FJ
    Parashar, P
    [J]. JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 2000, 33 (17): : 3445 - 3465
  • [6] Classification of four-dimensional real Lie bialgebras of symplectic type and their Poisson–Lie groups
    J. Abedi-Fardad
    A. Rezaei-Aghdam
    Gh. Haghighatdoost
    [J]. Theoretical and Mathematical Physics, 2017, 190 : 1 - 17
  • [7] Poisson-Lie T-duality for quasitriangular Lie bialgebras
    Beggs, EJ
    Majid, S
    [J]. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2001, 220 (03) : 455 - 488
  • [8] THREE DIMENSIONAL REAL LIE BIALGEBRAS
    Farinati, Marco A.
    Patricia Jancsa, A.
    [J]. REVISTA DE LA UNION MATEMATICA ARGENTINA, 2015, 56 (01): : 27 - 62
  • [9] Classical deformations, Poisson-Lie contractions, and quantization of dual Lie bialgebras
    Ballesteros, A.
    Herranz, F. J.
    Del Olmo, M. A.
    Santander, M.
    [J]. Journal of Mathematical Physics, 36 (02):
  • [10] CLASSICAL DEFORMATIONS, POISSON-LIE CONTRACTIONS, AND QUANTIZATION OF DUAL LIE BIALGEBRAS
    BALLESTEROS, A
    HERRANZ, FJ
    DELOLMO, MA
    SANTANDER, M
    [J]. JOURNAL OF MATHEMATICAL PHYSICS, 1995, 36 (02) : 631 - 640
12345