Inner Superderivation of n-Isoclinism Lie Superalgebras

In this paper, we consider any two ideals I and J of a finite-dimensional Lie superalgera G . Then we define the set Sder J I ( G ) , which contains the set of all superderivations of G which take J to zero and whose images are contained in I and the set Sder c n ( G ) , which contains the set of all superderivations δ of G such that δ ( g ) ∈ [ g , G n ] for all g ∈ G . In this article, we have shown that if ( φ , θ ) is an n -isoclinism between two finite-dimensional Lie superalgebras G and H , then there exists an isomorphism from Sder Z n ( G ) G n + 1 ( G ) to Sder Z n ( H ) H n + 1 ( H ) . Also, we prove the necessary and sufficient conditions under which Sder c n ( G ) is isomorphic to certain special subsuperalgebras of Sder ( G ) .