2-Local Superderivations On Strictly Semi-simple Lie Superalgebras Spl(n,m)

The construction of derivations of Lie algebras is one of main topics of Lie algebras’con-struction research. So are the construction of superderivations of Lie super algebras. The purpose of this paper is to study the construction of 2-local superderivations on strictly semi-simple Lie superalgebras spl(n, m)(n≠ m) over algebraically closed fields of characteristic zero.In resent years, a lot of scholars have researched derivation algebras and generalized the definition of derivations and proposed the conception of local derivations and 2-local derivations. Furthermore, it was researched that the properties of local derivations and 2-local derivations on some Lie algebras which have some special properties. Recently, mathematicians have already made a progress in the investigations of derivations and 2-local derivations of Lie algebras. Therefore, the theories of local derivations and 2-local derivations of Lie algebras have been more and more perfect.However, little research has been done in the properties of local superderivations and 2-local superderivations on Lie superalgebras. So the results of local superderivations and 2-local superderivations are not enough. For the construction of 2-local superderivations of Lie su-peralgebras, the problem we are most concerned about is whether 2-local superderivations are superderivations. This paper gives the definition of 2-local superderivations. By some properties of strictly semi-simple Lie superalgebras spl(n, m) (n≠ m), which are semi-simplicity. Cartan subalgebra. root space decomposition and so on. the paper proves that all 2-local superderiva-tions on Lie superalgebras spl(n, m) (n≠ m) are superderivations and they are linear.