On the Ricci curvature of nonunimodular solvable metric Lie algebras of small dimension

被引：0
|
作者：
Chebarykov M.S. [1 ]
机构：
[1] Rubtsovsk Industrial Institute
来源：
Siberian Advances in Mathematics | 2011年 / 21卷 / 2期
关键词：
homogeneous Riemannian manifold; left-invariant Riemannian metric; Lie algebra; Lie group; the Ricci curvature;
D O I：
10.3103/S1055134411020015
中图分类号：
学科分类号：
摘要：
The Ricci curvature of solvable metric Lie algebras is studied. In particular, we prove that the Ricci operator of any metric nonunimodular solvable Lie algebra of dimension not exceeding 6 has at least two negative eigenvalues, that generalizes the known results. © 2011 Allerton Press, Inc.
引用
收藏
页码：81 / 99
页数：18
相关论文
共 50 条
  • [21] On Lie Groups with Recurrent Curvature in Dimension Four
    Milad Bastami
    Amirhesam Zaeim
    Ali Haji-Badali
    Bulletin of the Iranian Mathematical Society, 2022, 48 : 1037 - 1049
  • [22] Constructions of metric (n + 1)-Lie algebras
    Ruipu Bai
    Shuangshuang Chen
    Chinese Annals of Mathematics, Series B, 2016, 37 : 729 - 742
  • [23] ON BEHAVIOR OF SOLVABLE IDEALS OF LIE ALGEBRAS UNDER OUTER DERIVATIONS
    Petravchuk, Anatoliy P.
    COMMUNICATIONS IN ALGEBRA, 2010, 38 (06) : 2311 - 2316
  • [24] A graph theoretical determination of solvable complete rigid Lie algebras
    Campoamor-Stursberg, R
    LINEAR ALGEBRA AND ITS APPLICATIONS, 2003, 372 : 53 - 66
  • [25] Solvable Leibniz algebras with quasi-filiform Lie algebras of maximum length nilradicals
    Muratova, Kh. A.
    Ladra, M.
    Omirov, B. A.
    Sattarov, A. M.
    COMMUNICATIONS IN ALGEBRA, 2020, 48 (08) : 3525 - 3542
  • [26] Some results on metric n-Lie algebras
    Rui Pu Bai
    Wan Qing Wu
    Zhen Heng Li
    Acta Mathematica Sinica, English Series, 2012, 28 : 1209 - 1220
  • [27] Algorithmic construction of solvable rigid Lie algebras determined by generating functions
    Campoamor-Stursberg, R.
    Oviano Garcia, F.
    LINEAR & MULTILINEAR ALGEBRA, 2022, 70 (02) : 280 - 296
  • [28] Cohomologically rigid solvable Lie algebras with a nilradical of arbitrary characteristic sequence
    Ancochea Bermudez, J. M.
    Campoamor-Stursberg, R.
    LINEAR ALGEBRA AND ITS APPLICATIONS, 2016, 488 : 135 - 147
  • [29] ON THE DIMENSION OF A SPECIAL SUBALGEBRA OF DERIVATIONS OF NILPOTENT LIE ALGEBRAS
    Sheikh-Mohseni, S.
    Saeedi, F.
    BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY, 2017, 43 (01): : 79 - 93
  • [30] Combinatorial structures associated with Lie algebras of finite dimension
    Carriazo, A
    Fernández, LM
    Núñez, J
    LINEAR ALGEBRA AND ITS APPLICATIONS, 2004, 389 : 43 - 61
12345