Super Triple Derivations Of A Class Of Filiform Lie Superalgebras Q_2m,2m

The related research of Lie superalgebras has attracted much attention from scholars,as a special Lie superalgebras,nilpotent Lie superalgebras,is one of the important research topics in Lie superalgebras.A class of nilpotent Lie algebras Fil-iform Lie algebras with important properties was proposed by Vergne in the 1960s.Later,two scholars J.Berm'udez,O.Campoamor introduced a class of Filiform Lie superalgebras Q_2m,2mwhose even part is Filiform Lie algebras Q_2m.The study of derivations and superderivations is also an important research topic in the field of mathematics.With the progress of research,scholars have popularized the concept of derivations and obtained the concept of triple derivations.The research on the structural properties of triple derivations in other algebras has also attracted extensive attention.In this paper,we study the super triple derivations of Q_2m,2m.Starting from the relevant properties of super triple derivations,according to the structure of Q_2m,2m,several special super triple derivations of Q_2m,2mare found by calculation.And then the linear independence of these special super triple derivations is proved,it is explained that any super triple derivations can be linearly represented by the above special super triple derivations,the space structure and algebraic structure of super triple derivations of Q_2m,2mis characterized.