Résumé
Let D be a simple derivation of the polynomial ring k [x(1), ... , x(n)], where Ill is an algebraically closed field of characteristic zero, and denote by Aut(D) subset of Aut(k [x(1),... , x(n)]) the subgroup of Ill-automorphisms commuting with D. We show that the connected component of Aut(D) passing through the identity is a unipotent algebraic group of dimension at most n-2, this bound being sharp. Moreover, Aut(D) is an algebraic group if and only if it is a connected ind-group. Given a simple derivation D, we characterize when Aut(D) contains a normal subgroup of translations. As an application of our techniques we show that if n = 3, then either Aut(D) is a discrete group or it is isomorphic to the additive group acting by translations, and give some insight on the case n = 4. (c) 2025 Elsevier B.V. All rights are reserved, including those for text and data mining, AI training, and similar technologies.