Rotr-Baxter Operators And The Multiplicative Hom-Structures Of A Class Of Filiform Lie Superalgebras Q_2m,2m

Nilpotent Lie superalgebra is an important research topic in Lie superalgebra.In the 1960s,Vergne first proposed the definition of Filiform Lie algebra,which is a special class of nilpotent Lie algebras[1].As a deformation of Filiform Lie algebras,Q2m is one of the only two classes of Filiform Lie algebras with natural gradation.In 2002,Bermude and Campoam made natural generalization of Lie algebra Q2m and introduced a class of Filiform Lie superalgebra Q2m,2m whose even part is Q2m[2].In this paper,we mainly study the Hom-structures as well as the Rota-Baxter operators of Filiform Lie superalgebra.Firstly,we calculate the Rota-Baxter op-erators of the eight-dimensional Lie superalgebra Q4,4 with zero weight.Secondly,we use the existing Hom-structures of Q2m,2m to further study its multiplicative Hom-structures and give its matrix form.