Derivations from the Even Parts into the Odd Parts for Lie Superalgebras W and S

Let W and S denote the even parts of the generalized Witt superalgebra W and the special superalgebra S over a field of characteristic p > 3 , respectively.In this note, using the method of reduction on Z-gradations, we determine the derivation space Der(W, W 1 ) from W into W 1 and the derivation space Der(S, W 1 ) from S into W 1 .In particular, the derivation space Der(S, S 1 ) is determined.