On simple Shamsuddin derivations in two variables

Abstract

We study the subgroup of k -automorphisms of k ⁢ [ x , y ] which commute with a simple derivation d of k ⁢ [ x , y ] . We prove, for instance, that this subgroup is trivial when d is a shamsuddin simple derivation. in the general case of simple derivations, we obtain properties for the elements of this subgroup.