2-local derivations on the Jacobson-Witt algebras in prime characteristic

TL;DR

This paper investigates 2-local derivations on simple Jacobson-Witt Lie algebras over fields of prime characteristic, proving that all such 2-local derivations are actually derivations, thus extending understanding of their structure.

Contribution

It establishes that every 2-local derivation on simple Jacobson-Witt algebras in prime characteristic is a derivation, a new result in the structure theory of these algebras.

Findings

All 2-local derivations on the algebra are derivations.

The result applies to Jacobson-Witt algebras over fields with characteristic p.

The study advances the understanding of derivation structures in modular Lie algebras.

Abstract

This paper initiates the study of 2-local derivations on Lie algebras over fields of prime characteristic. Let $\mathfrak{g}$ be a simple Jacobson-Witt algebra $W_n$ over a field of prime characteristic $p$ with cardinality no less than $p^n$. In this paper, we study properties of 2-local derivations on $\mathfrak{g}$, and show that every 2-local derivation on $\mathfrak{g}$ is a derivation.