Lie Superalgebras Based On Filiform Lie Algebras Of Type L_n

Starting from Lie algebras,the Lie algebras module and symmetric bilinear maps are used to construct Lie superalgebras whose even part is a given Lie algebras and whose odd part is a given module,which is of great significance in theory of Lie superalgebras.At the same time,the classification of Lie superalgebras in the sense of isomorphism is an important topic of Lie theory.In this paper,we construct a class of Lie superalgebras whose even part is Filiform Lie algebras of typeL_n,and whose odd part is adjoint module of even part.They are called Lie superalgebras based on Filiform Lie algebras of typeL_n.Furthermore,the complete classification of Lie superalgebras based on Filiform Lie algebras of typeL_nis given by using the classification theory of orbits acting on groups and matrices in the sense of contract.