Artin–Hasse exponentials of derivations

We show how Artin–Hasse exponentials of nilpotent derivations can be used to produce new cyclic gradings of non-associative algebras of prime characteristic from a given one. We discuss the connection with the technique of switching tori (and, consequently, the associated root space decompositions) in restricted modular Lie algebras. However, differently from toral switching, our method can produce gradings over cyclic p-groups of order higher than p. In particular, we apply it to construct cyclic gradings of the Zassenhaus Lie algebra of dimension pn, for p>3.