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 isomorp...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.展开更多
文摘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.
