The group of automorphisms of the Lie algebra of derivations of a field of rational functions

TL;DR

This paper proves that the automorphism group of the Lie algebra of derivations of a rational function field is isomorphic to the automorphism group of the field itself, establishing a canonical correspondence.

Contribution

It establishes a canonical isomorphism between the automorphism group of the Lie algebra of derivations and the automorphism group of the rational function field.

Findings

Automorphism group of the Lie algebra is isomorphic to that of the field.

Provides a canonical isomorphism between these automorphism groups.

Enhances understanding of symmetries in derivation Lie algebras.

Abstract

We prove that the group of automorphisms of the Lie algebra $\Der_K (Q_n)$ of derivations of the field of rational functions $Q_n=K(x_1,..., x_n)$ over a field of characteristic zero is canonically isomorphic to the group of automorphisms of the $K$-algebra $Q_n$.