Quasi-trace functions on Lie algebras and their applications to 3-Lie algebras

被引：2
|
作者：
Tan, Youjun [1 ]
Xu, Senrong [2 ]
机构：
[1] Sichuan Univ, Math Coll, 24 South Sect 1,Yihuan Rd, Chengdu 610064, Peoples R China
[2] Jiangsu Univ, Sch Math Sci, 301 Xuefu Rd, Zhenjiang 212013, Jiangsu, Peoples R China
来源：
CZECHOSLOVAK MATHEMATICAL JOURNAL | 2022年 / 72卷 / 02期
关键词：
quasi-trace function; 3-Lie algebra; Leibniz algebra; COHOMOLOGY; EXTENSIONS; LEIBNIZ; IDEALS;
D O I：
10.21136/CMJ.2022.0059-21
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We introduce the notion of quasi-trace functions on Lie algebras. As applications we study realizations of 3-dimensional and 4-dimensional 3-Lie algebras. Some comparison results on cohomologies of 3-Lie algebras and Leibniz algebras arising from quasi-trace functions are obtained.
引用
收藏
页码：559 / 591
页数：33
相关论文
共 50 条
  • [41] Induced 3-Lie algebras, superalgebras and induced representations
    Abramov, Viktor
    Latt, Priit
    PROCEEDINGS OF THE ESTONIAN ACADEMY OF SCIENCES, 2020, 69 (02) : 116 - 133
  • [42] The Wells Map for Abelian Extensions of 3-Lie Algebras
    Youjun Tan
    Senrong Xu
    Czechoslovak Mathematical Journal, 2019, 69 : 1133 - 1164
  • [43] Extensions and Deformations of 3-Lie Algebras with Higher Derivations
    Shuangjian GUO
    Journal of Mathematical Research with Applications, 2025, 45 (01) : 20 - 32
  • [44] A unified approach to controlling algebras and cohomologies of various operators on 3-Lie algebras
    Hou, Shuai
    Sheng, Yunhe
    Zhou, Yanqiu
    INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS, 2025,
  • [45] Deformations and Extensions of Modified λ-Differential 3-Lie Algebras
    Teng, Wen
    Zhang, Hui
    MATHEMATICS, 2023, 11 (18)
  • [46] On Non-Abelian Extensions of 3-Lie Algebras
    宋丽娜
    Abdenacer Makhlouf
    唐荣
    CommunicationsinTheoreticalPhysics, 2018, 69 (04) : 347 - 356
  • [47] The Realization of 4-dimensional 3-Lie Algebras
    刘建波
    张艳艳
    张知学
    Northeastern Mathematical Journal, 2007, (03) : 247 - 254
  • [48] Symplectic, product and complex structures on 3-Lie algebras
    Sheng, Yunhe
    Tang, Rong
    JOURNAL OF ALGEBRA, 2018, 508 : 256 - 300
  • [49] 3-post-Lie algebras and relative Rota-Baxter operators of nonzero weight on 3-Lie algebras
    Hou, Shuai
    Sheng, Yunhe
    Zhou, Yanqiu
    JOURNAL OF ALGEBRA, 2023, 615 : 103 - 129
  • [50] Classification of transposed Poisson 3-Lie algebras of dimension 3
    Jiang, Yaxi
    Kang, Chuangchuang
    Lu, Jiafeng
    COMMUNICATIONS IN ALGEBRA, 2025,
12345