NAMBU STRUCTURES ON FOUR-DIMENSIONAL REAL LIE GROUPS AND RELATED SUPERINTEGRABLE SYSTEMS

被引：0
作者：
Farhang-Sardroodi, S. [1 ]
Rezaei-Aghdam, A. [1 ]
Sedghi-Ghadim, L. [2 ]
机构：
[1] Azarbaijan Shahid Madani Univ, Dept Phys, Tabriz, Iran
[2] Azarbaijan Shahid Madani Univ, Dept Math, Tabriz, Iran
来源：
THEORETICAL AND MATHEMATICAL PHYSICS | 2015年 / 183卷 / 02期
关键词：
Nambu structure; superintegrable system; Lie group; GENERALIZED POISSON STRUCTURES; ALGEBRAS; MECHANICS; MANIFOLDS; BRACKETS; DYNAMICS;
D O I：
10.1007/s11232-015-0288-9
中图分类号：
O4 [物理学];
学科分类号：
0702 ;
摘要：
We determine all third- and fourth-order Nambu tensors (Nambu structures) on four-dimensional real Lie groups. In addition, we obtain superintegrable systems using the fourth-order Nambu structures on some of these Lie groups as phase spaces with the symmetry groups A(4,8) and A(4,10).
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页码：684 / 704
页数：21
相关论文
共 24 条
  • [1] Integrable and superintegrable Hamiltonian systems with four dimensional real Lie algebras as symmetry of the systems
    Abedi-Fardad, J.
    Rezaei-Aghdam, A.
    Haghighatdoost, Gh.
    [J]. JOURNAL OF MATHEMATICAL PHYSICS, 2014, 55 (05)
  • [2] ALEKSEEVSKY D, 1996, ACTA MATH U COMENIAN, V65, P1
  • [3] Bolsinov A. V., 1999, Integrable Hamiltonian systems. Geometry, topology, classification
  • [4] Classical and quantum Nambu mechanics
    Curtright, T
    Zachos, C
    [J]. PHYSICAL REVIEW D, 2003, 68 (08)
  • [5] New generalized Poisson structures
    deAzcarraga, JA
    Perelomov, AM
    Bueno, JCP
    [J]. JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 1996, 29 (07): : L151 - L157
  • [6] On the higher-order generalizations of Poisson structures
    deAzcarraga, JA
    Izquierdo, JM
    Bueno, JCP
    [J]. JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 1997, 30 (18): : L607 - L616
  • [7] The Schouten-Nijenhuis bracket, cohomology and generalized Poisson structures
    deAzcarraga, JA
    Perelomov, AM
    Bueno, JCP
    [J]. JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 1996, 29 (24): : 7993 - 8009
  • [8] Some remarks concerning Nambu mechanics
    Gautheron, P
    [J]. LETTERS IN MATHEMATICAL PHYSICS, 1996, 37 (01) : 103 - 116
  • [9] Remarks on Nambu-Poisson and Nambu-Jacobi brackets
    Grabowski, J
    Marmo, G
    [J]. JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 1999, 32 (23): : 4239 - 4247
  • [10] On Filippov algebroids and multiplicative Nambu-Poisson structures
    Grabowski, J
    Marmo, G
    [J]. DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS, 2000, 12 (01) : 35 - 50
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