The group of automorphisms of the Lie algebra of derivations of a polynomial algebra

TL;DR

This paper proves that the automorphism group of the Lie algebra of derivations of a polynomial algebra over a field of characteristic zero is isomorphic to the automorphism group of the polynomial algebra itself, establishing a deep structural link.

Contribution

It establishes a canonical isomorphism between the automorphism group of the derivation Lie algebra and the automorphism group of the polynomial algebra, a novel structural result.

Findings

Automorphism group of derivations is isomorphic to polynomial algebra automorphisms

Provides a canonical isomorphism between these automorphism groups

Deepens understanding of the algebraic structure of derivations

Abstract

We prove that the group of automorphisms of the Lie algebra $\Der_K (P_n)$ of derivations of a polynomial algebra $P_n=K[x_1,..., x_n]$ over a field of characteristic zero is canonically isomorphic to the the group of automorphisms of the polynomial algebra $P_n$.