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
  • [1] Quasi-trace functions on Lie algebras and their applications to 3-Lie algebras
    Youjun Tan
    Senrong Xu
    Czechoslovak Mathematical Journal, 2022, 72 : 559 - 591
  • [2] Some Results on Quasi-Trace Functions on (Pre-)Lie Algebras
    Chen, Ming
    Wang, Qi
    Xu, Senrong
    JOURNAL OF LIE THEORY, 2022, 32 (02) : 413 - 430
  • [3] 3-Lie∞-algebras and 3-Lie 2-algebras
    Zhou, Yanqiu
    Li, Yumeng
    Sheng, Yunhe
    JOURNAL OF ALGEBRA AND ITS APPLICATIONS, 2017, 16 (09)
  • [4] Extending structures for 3-Lie algebras
    Zhang, Tao
    COMMUNICATIONS IN ALGEBRA, 2022, 50 (04) : 1469 - 1497
  • [5] On 3-Lie algebras with a derivation
    Guo S.
    Saha R.
    Afrika Matematika, 2022, 33 (2)
  • [6] On 3-lie algebras with a derivation
    Guo, Shuangjian
    Saha, Ripan
    AFRIKA MATEMATIKA, 2022, 33 (02)
  • [7] Cohomology and deformations of 3-Lie colour algebras
    Zhang, Tao
    LINEAR & MULTILINEAR ALGEBRA, 2015, 63 (04) : 651 - 671
  • [8] Representations and cohomologies of differential 3-Lie algebras with any weight and applications
    Sun, Qinxiu
    Li, Zhen
    Chen, Shan
    JOURNAL OF ALGEBRA AND ITS APPLICATIONS, 2025, 24 (07)
  • [9] Transposed Poisson algebras, Novikov-Poisson algebras and 3-Lie algebras
    Bai, Chengming
    Bai, Ruipu
    Guo, Li
    Wu, Yong
    JOURNAL OF ALGEBRA, 2023, 632 : 535 - 566
  • [10] On Non-Abelian Extensions of 3-Lie Algebras
    Song, Li-Na
    Makhlouf, Abdenacer
    Tang, Rong
    COMMUNICATIONS IN THEORETICAL PHYSICS, 2018, 69 (04) : 347 - 356
12345