首页|On non-abelian extensions of 3-Leibniz algebras
On non-abelian extensions of 3-Leibniz algebras
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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.
3-Leibniz algebrasLeibniz algebranon-abelian extensionMaurer-Cartan element
Nanyan XU、Yunhe SHENG
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School of Mathematics,Jilin University,Changchun 130012,China
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