The groups of automorphisms of the Lie algebras of polynomial vector fields with zero or constant divergence

TL;DR

This paper determines the automorphism groups of Lie algebras consisting of polynomial vector fields with zero or constant divergence, advancing understanding of their symmetries.

Contribution

It explicitly characterizes the automorphism groups for these Lie algebras, a novel result in the study of polynomial vector fields.

Findings

Automorphism group for vector fields with zero divergence identified

Automorphism group for vector fields with constant divergence characterized

Provides new insights into symmetries of polynomial vector fields

Abstract

The group of automorphisms is found for the Lie algebra of polynomial vector fields with constant divergence.