On the nilpotency of a pair of Lie algebras

被引：0
|
作者：
Gholamian, Ali [1 ]
Eghdami, Hossein [2 ]
机构：
[1] Farhangian Univ, Dept Math, Shahid Bahonar Campus, Birjand, Iran
[2] Univ Birjand, Dept Math, Birjand, Iran
来源：
MATEMATIKA | 2016年 / 32卷
关键词：
Pair of Lie algebras; nilpotent Lie algebras; central series;
D O I：
暂无
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we introduce the new concepts of nilpotency, upper and lower central series for a pair of Lie algebras (L, N), in which N is an ideal of Lie algebra L. We study the properties of these concepts and prove the analogue of Robinson Theorem for a pair of Lie algebras plays an important role to find the results connecting to the idea of nilpotency in the pair of Lie algebras. In particular we find a criterion such that an extension of pair of Lie algebras can be nilpotent.
引用
收藏
页码：1 / 5
页数：5
相关论文
共 50 条
  • [1] On the semigroup nilpotency and the Lie nilpotency of associative algebras
    A. N. Krasil'nikov
    Mathematical Notes, 1997, 62 : 426 - 433
  • [2] On the semigroup nilpotency and the Lie nilpotency of associative algebras
    Krasil'nikov, AN
    MATHEMATICAL NOTES, 1997, 62 (3-4) : 426 - 433
  • [3] The Nilpotency of Lie Triple Algebras
    WANG Gui-dong (Institute of Applied Mathematics
    Graduate School of the Chinese Academy of Sciences
    数学季刊, 2005, (04) : 423 - 429
  • [4] Spectral conditions for the nilpotency of Lie algebras
    Beltita, D
    JOURNAL OF OPERATOR THEORY, 2001, 46 (03) : 593 - 603
  • [5] Nilpotency criteria for multiplicative Lie algebras
    Point, F
    Wantiez, P
    JOURNAL OF PURE AND APPLIED ALGEBRA, 1996, 111 (1-3) : 229 - 243
  • [6] Nilpotency and capability in multiplicative Lie algebras
    Kumar, Amit
    Pandey, Mani Shankar
    Upadhyay, Sumit Kumar
    COMMUNICATIONS IN ALGEBRA, 2024, 52 (09) : 3799 - 3811
  • [7] Lie commutator, solvability and nilpotency in multiplicative Lie algebras
    Pandey, Mani Shankar
    Lal, Ramji
    Upadhyay, Sumit Kumar
    JOURNAL OF ALGEBRA AND ITS APPLICATIONS, 2021, 20 (08)
  • [8] Lie nilpotency and Lie solvability of tensor product of multiplicative Lie algebras
    Pal, Deepak
    Kumar, Amit
    Upadhyay, Sumit Kumar
    Kushwaha, Seema
    COMMUNICATIONS IN ALGEBRA, 2025, 53 (03) : 1296 - 1306
  • [9] Group algebras of Lie nilpotency index 14
    Bhatt, Suchi
    Chandra, Harish
    Sahai, Meena
    ASIAN-EUROPEAN JOURNAL OF MATHEMATICS, 2020, 13 (05)
  • [10] SOME CRITERIA FOR NILPOTENCY IN GROUPS AND LIE ALGEBRAS
    SCHENKMA.E
    PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1969, 21 (03) : 714 - +
12345