On non-abelian extensions of 3-Leibniz algebras

doi:10.3868/s140-DDD-024-0006-x

Frontiers of Mathematics in China

2024, Vol. 19

Issue (2): 57-74 https://doi.org/10.3868/s140-DDD-024-0006-x

本期目录

On non-abelian extensions of 3-Leibniz algebras

Nanyan XU(

), Yunhe SHENG(

)

School of Mathematics, Jilin University, Changchun 130012, China

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Abstract：

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.

Key words： 3-Leibniz algebras Leibniz algebra non-abelian extension Maurer-Cartan element

出版日期: 2024-06-11

Corresponding Author(s): Nanyan XU,Yunhe SHENG

引用本文:

. [J]. Frontiers of Mathematics in China, 2024, 19(2): 57-74.
Nanyan XU, Yunhe SHENG. On non-abelian extensions of 3-Leibniz algebras. Front. Math. China, 2024, 19(2): 57-74.

链接本文:

https://academic.hep.com.cn/fmc/CN/10.3868/s140-DDD-024-0006-x
https://academic.hep.com.cn/fmc/CN/Y2024/V19/I2/57

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