摘要
本文主要利用Maurer-Cartan元研究3-莱布尼茨代数的非交换扩张.我们构造了一个微分分次李代数,并且证明了这个微分分次李代数上的Maurer-Cartan元等价类与3-莱布尼茨代数的非交换扩张同构类是一一对应的.同时分析了由3-莱布尼茨代数基本元所构成空间上的莱布尼茨代数结构,证明了一个3-莱布尼茨代数的非交换扩张诱导了一个莱布尼茨代数的非交换扩张.
In this paper,we study non-abelian extensions of 3-Leibniz algebras through Maurer-Cartan elements.We construct a differential graded Lie algebra and prove that there is a one-to-one correspondence between isomorphism classes of non-abelian extensions of 3-Leibniz algebras and equivalence classes of Maurer-Cartan elements in this differential graded Lie algebra.We also analyze the Leibniz algebra structure on the space of fundamental objects of 3-Leibniz algebras,and show that a non-abelian extension of 3-Leibniz algebras naturally induces a nonabelian extension of Leibniz algebras.
作者
徐楠燕
生云鹤
XU Nanyan;SHENG Yunhe(School of Mathematics,Jilin University,Changchun,Jilin,130012,P.R.China)
出处
《数学进展》
CSCD
北大核心
2023年第6期1048-1062,共15页
Advances in Mathematics（China）
基金
国家自然科学基金(No.11922110)
