The Hom-structures And The Multiplicative Hom-structures Of (N-3)-filiform Lie Algebras

The construction of Lie algebras is one of main topics of Lie algebras research.The purpose of this paper is to study the construction of a kind of Lie algebras.It is well known that the Lie algebras research can be simplified to semi-simple and solvable Lie algebras research by Levi's theorem.And the solvable Lie algebras can be due to the nilpotent Lie algebras.Nilpotent Lie algebras is a very important class of Lie Algebras in Lie theory.The research on Hom-Lie algebras firstly comes from the dual needs of Lie algebras and physics,which is mainly related to the quantum deformation of Lie algebras and physics,especially vector field Lie algebras.In recent years,some progress has been made in the study of Hom-Lie algebras and Hom-structures of Lie algebras.Since the structures of nilpotent Lie algebras play an important role in the theory of Lie algebras,we mainly consider the Hom-structures and the multiplicative Hom-structures of p-filiform Lie algebras in this paper.And we characterize the Hom-structures and the multi-plicative Hom-structures of(n-3)-filiform Lie algebras(n ? 5)in terms of matrices.