On the tame isotropy group of a derivation

TL;DR

This paper introduces and studies the tame isotropy group of a derivation in polynomial rings, focusing on specific classes of derivations across different variable counts.

Contribution

It defines the tame isotropy group for derivations and analyzes its structure for triangular, simple, and Shamsuddin derivations in polynomial rings.

Findings

Characterization of the tame isotropy group for triangular derivations

Analysis of the tame isotropy group for simple derivations in two variables

Study of the tame isotropy group for Shamsuddin derivations in any polynomial ring

Abstract

We introduce the tame isotropy group of a derivation of a polynomial ring. We study this group for certain triangular derivations up to three variables, for simple derivations in two variables, and for simple Shamsuddin derivations in any polynomial ring.