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 $0$.

Dedicated to Lê Dũng Tráng; final version; 2 references added; minor corrections. arXiv admin note: text overlap with arXiv:1807.10193, arXiv:1903.08985