On non-abelian extensions of 3-Leibniz algebras  

作　　者：Nanyan XU Yunhe SHENG 

机构地区：[1]School of Mathematics,Jilin University,Changchun 130012,China

出　　处：《Frontiers of Mathematics in China》2024年第2期57-74,共18页中国高等学校学术文摘·数学（英文）

摘　　要：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 the isomorphism classes of non-abelian extensions in 3-Leibniz algebras and the equivalence classes of Maurer-Cartan elements in this differential graded Lie algebra.And also the Leibniz algebra structure on the space of fundamental elements of 3-Leibniz algebras is analyzed.It is proved that the non-abelian extension of 3-Leibniz algebras induce the non-abelian extensions of Leibniz algebras.

关 键 词：3-Leibniz algebras Leibniz algebra non-abelian extension Maurer-Cartan element 

分 类 号：O15[理学—数学]