Derivations of the even part of contact Lie superalgebra

Let K and W denote the even parts of the contact Lie superalgebra and the generalized Witt Lie superalgebra respectively. In the paper, the 1-cocycle of K with values in K-moduleW is studied. In particular, the negative homogeneous 1-cocycle of K with values in K-moduleW is determined and as an application, the negative homogeneous 1-cocycle of K is given. For the nonnegative homogeneous 1-cocycle of K with values in W, we first give reduction theorem and then determine the nonnegative homogeneous 1-cocycle of K with values in K-module W.