On generalizations of derivations of lie superalgebras

The main theme of this paper is to study some basic concepts of G-superderivations of a Lie superalgebra L. In particular, under certain condition, Sder(L) ⊕ Sderθ (L) forms a Lie superalgebra. As one of the important results, we have defined a bilinear product concerned with G-superderivations that actually gives rise to a left symmetric superalgebraic structure.