Local derivations on the Lie algebra $W(2,2)$

TL;DR

This paper proves that all local derivations on the Lie algebra $W(2,2)$ are actual derivations, and applies this result to classify local derivations on the deformed $ms_3$ algebra.

Contribution

It establishes that every local derivation on $W(2,2)$ is a derivation and extends this to the deformed $ms_3$ algebra, providing a complete classification.

Findings

All local derivations on $W(2,2)$ are derivations.

Classification of local derivations on the deformed $ms_3$ algebra.

Use of linear algebra methods and key constructions in the proof.

Abstract

The present paper is devoted to studying local derivations on the Lie algebra $W(2,2)$ which has some outer derivations. Using some linear algebra methods in \cite{CZZ} and a key construction for $W(2,2)$ we prove that every local derivation on $W(2, 2)$ is a derivation. As an application, we determine all local derivations on the deformed $\mathfrak{bms}_3$ algebra.