Central extensions of restricted Lie superalgebras and classification of p-nilpotent Lie superalgebras in dimension 4

The first main result of this paper is to build the first and second restricted cohomology groups for restricted Lie superalgebras in characteristic [Formula: see text], modifying a construction by Yuan, Chen and Cao. We will explain how these groups capture some algebraic structures, such as extensions and derivations. Further, we apply this construction to classify [Formula: see text]-nilpotent restricted Lie superalgebras up to dimension [Formula: see text] over an algebraically closed field of characteristic [Formula: see text].