Cohomology of Zassenhaus superalgebras with coefficients in generalized restricted Kac modules

Over a field of characteristic [Formula: see text], we study the cohomology of the Zassenhaus superalgebra with coefficients in generalized restricted Kac modules [Formula: see text]. First, the structure of [Formula: see text] and the weight space decompositions are given. Next, the weight-derivations of the Zassenhaus superalgebra to [Formula: see text] are computed. Finally, the zeroth and first cohomology groups of the Zassenhaus superalgebra with coefficients in [Formula: see text] are determined.