预李代数的交叉模  

Crossed Module of Pre-Lie Algebras

作　　者：孙聚波 张庆成[2] SUN Jubo;ZHANG Qingcheng(Faculty of Applied Sciences,Jilin Engineering Normal University,Changchun 130052,China;School of Mathematics and Statistics,Northeast Normal University,Changchun 130024,China)

机构地区：[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

出　　处：《吉林大学学报（理学版）》2022年第3期604-608,共5页Journal of Jilin University:Science Edition

基　　金：国家自然科学基金(批准号:11671069);吉林省教育厅“十三五”科学技术研究规划项目(批准号:JJLH20200170KJ).

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cat^(1)-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.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 cat 1-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.

关 键 词：预李代数 交叉模 作用 同态 群胚 

分 类 号：O152.5[理学—数学]