On generalized derivations of polynomial vector fields Lie algebras

TL;DR

This paper investigates the structure of generalized derivations within specific Lie sub-algebras of polynomial vector fields on Euclidean space, focusing on those containing constant and Euler vector fields, under certain conditions.

Contribution

It characterizes generalized derivations of Lie sub-algebras of polynomial vector fields that include constant and Euler vector fields, expanding understanding of their algebraic structure.

Findings

Identification of conditions under which generalized derivations are characterized

Extension of derivation theory to polynomial vector field Lie algebras

Insights into the algebraic structure of these Lie sub-algebras

Abstract

In this paper, we study the generalized derivation of a Lie sub-algebra of the Lie algebra of polynomial vector fields on $\mathbb{R}^n$ where $n\geq1$, containing all constant vector fields and the Euler vector field, under some conditions on this Lie sub-algebra.