| 预李代数的交叉模 |
| |
| 引用本文： | 孙聚波,张庆成.预李代数的交叉模[J].吉林大学学报(理学版),2022,60(3):604-608. |
| |
| 作者姓名： | 孙聚波 张庆成 |
| |
| 作者单位： | 1. 吉林工程技术师范学院 应用理学院, 长春 130052; 2. 东北师范大学 数学与统计学院, 长春 130024 |
| |
| 摘 要： | 首先, 给出预李代数作用的定义及交叉模的定义, 并研究交叉模的相关性质; 其次, 利用交叉模的定义和预李代数的半直积给出预李代数交叉模的同构类与cat1-预李代数的同构类是等价的结果; 最后, 给出交叉模的同态和同态的同伦构成一个群胚结构.
|
| 关 键 词： | 预李代数 交叉模 作用 同态 群胚 |
| 收稿时间： | 2021-08-23 |
Crossed Module of Pre-Lie Algebras |
| |
| SUN Jubo,ZHANG Qingcheng.Crossed Module of Pre-Lie Algebras[J].Journal of Jilin University: Sci Ed,2022,60(3):604-608. |
| |
| Authors: | SUN Jubo ZHANG Qingcheng |
| |
| Institution: | 1. Faculty of Applied Sciences, Jilin Engineering Normal University, Changchun 130052, China;
2. School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, China
|
| |
| Abstract: | Firstly, we gave the definitions of the action and the crossed module of pre-Lie algebras, and studied the related properties of the
crossed module. Secondly, a result was given that the isomorphism class of crossed modules of pre-Lie algebra was equivatent to that of cat1-pre-Lie algebras by using the definition of the crossed modules and semidirect product of pre-Lie algebras. Finally, we showed that the homomorphisms and their homotopies of crossed module formed a groupoid structure. |
| |
| Keywords: | pre-Lie algebra crossed module action homomorphism groupoid |
|
| 点击此处可从《吉林大学学报(理学版)》浏览原始摘要信息 |
| 点击此处可从《吉林大学学报(理学版)》下载免费的PDF全文 |
|
