Hasse–Schmidt derivations versus classical derivations

Abstract

In this paper we survey the notion and basic results on multivariate Hasse–Schmidt derivations over arbitrary commutative algebras and we associate to such an object a family of classical derivations. We study the behavior of these derivations under the action of substitution maps and we prove that, in characteristic 0, the original multivariate Hasse–Schmidt derivation can be recovered from the associated family of classical derivations. Our constructions generalize a previous one by M. Mirzavaziri in the case of a base field of characteristic 0.