Oriented tree diagram Lie algebras and their abelian ideals

被引:1
|
作者
Luo, Li [1 ]
机构
[1] E China Normal Univ, Dept Math, Shanghai 200241, Peoples R China
关键词
Abelian ideal; tree diagram; solvable Lie algebra; AD-NILPOTENT IDEALS; BOREL SUBALGEBRA; B-IDEALS; COHOMOLOGY;
D O I
10.1007/s10114-010-8455-2
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
We introduce oriented tree diagram Lie algebras which are generalized from Xu's both upward and downward tree diagram Lie algebras, and study certain numerical invariants of these algebras related to abelian ideals.
引用
收藏
页码:2041 / 2058
页数:18
相关论文
共 50 条
  • [11] Normalisers of Abelian Ideals of a Borel Subalgebra and Z-Gradings of a Simple Lie Algebra
    Panyushev, Dmitri I.
    JOURNAL OF LIE THEORY, 2016, 26 (03) : 659 - 672
  • [12] Ideals and conjugacy classes in solvable Lie algebras
    Ali, Sajid
    Azad, Hassan
    Biswas, Indranil
    M. Mahomed, Fazal
    INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS, 2023, 20 (12)
  • [13] SOLVABLE LIE ALGEBRAS AND MAXIMAL ABELIAN DIMENSIONS
    Tenorio, A. F.
    ACTA MATHEMATICA UNIVERSITATIS COMENIANAE, 2008, 77 (01): : 141 - 145
  • [14] Abelian ideals of a Borel subalgebra and subsets of the Dynkin diagram
    Panyushev, Dmitri I.
    JOURNAL OF ALGEBRA, 2011, 344 (01) : 197 - 204
  • [15] Algorithm to compute abelian subalgebras and ideals in Malcev algebras
    Ceballos, M.
    Nunez, J.
    Tenorio, A. F.
    MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2016, 39 (16) : 4892 - 4900
  • [16] Abelian subalgebras and ideals of maximal dimension in Poisson algebras
    Ouaridi, A. Fernandez
    Navarro, R. M.
    Towers, D. A.
    JOURNAL OF ALGEBRA, 2024, 660 : 680 - 704
  • [17] Abelian subalgebras and ideals of maximal dimension in Zinbiel algebras
    Ceballos, Manuel
    Towers, David A.
    COMMUNICATIONS IN ALGEBRA, 2023, 51 (04) : 1323 - 1333
  • [18] Split abelian chief factors and first degree cohomology for Lie algebras
    Feldvoss, Joerg
    Siciliano, Salvatore
    Weigel, Thomas
    JOURNAL OF ALGEBRA, 2013, 382 : 303 - 313
  • [19] VARIETIES OF ELEMENTARY ABELIAN LIE ALGEBRAS AND DEGREES OF MODULES
    Chang, Hao
    Farnsteiner, Rolf
    REPRESENTATION THEORY, 2021, 25 : 90 - 141
  • [20] Algorithm to compute the maximal abelian dimension of Lie algebras
    Ceballos, M.
    Nunez, J.
    Tenorio, A. F.
    COMPUTING, 2009, 84 (3-4) : 231 - 239