Hom-structures And Derivative Algebras Of A Class Of Filiform Lie Superalgebras Q_2m,2m

Nilpotent Lie superalgebras are a relatively recent research field within the Lie superalgebras.The filiform Lie algebras,a class of nilpotent Lie algebras with important properties,were introduced by Vergne in the sixties.Vergne showed that there are only two types of the so called naturally graded filiform Lie algebras Ln and Q2m.In 2002,Bermude and Campoam introduce a class of filiform Lie superalgebras Q2m,2m whose even part is Q2m.Hom-structures and derivation algebras of Lie superalgebras are active and important research topics.In this paper,We first describe the structure and the dimension of the derivative algebra of the filiform Lie superalgebra Q2m,2m·Next,by the Hom-Jocabi equation,we characterize the matrix forms and the dimension the Hom-structures of Q2m,2m.