On non-abelian extensions of 3-Leibniz algebras

  • Nanyan XU ,
  • Yunhe SHENG
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  • School of Mathematics, Jilin University, Changchun 130012, China
xuny20@mails.jlu.edu.cn
shengyh@jlu.edu.cn

Copyright

2024 Higher Education Press 2024

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.

Cite this article

Nanyan XU , Yunhe SHENG . On non-abelian extensions of 3-Leibniz algebras[J]. Frontiers of Mathematics in China, 2024 , 19(2) : 57 -74 . DOI: 10.3868/s140-DDD-024-0006-x

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