Cohomology of Zassenhaus superalgebras reveals structures in generalized restricted Kac modules, suggesting deeper algebraic relationships.
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]. Firstly, 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.
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Li et al. (2026) studied this question.
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