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

Qingyan Wu, Shoulan Gao, Dong Liu

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.

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

Abstract

The present paper is devoted to studying local derivations on the Lie algebra which has some outer derivations. Using some linear algebra methods in \cite{CZZ} and a key construction for we prove that every local derivation on is a derivation. As an application, we determine all local derivations on the deformed algebra.
Paper Structure (5 sections, 18 theorems, 46 equations)

This paper contains 5 sections, 18 theorems, 46 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Local derivations on the Witt subalgebra
  4. Local derivations on $W(2,2)$
  5. Local derivations on the deformed $\mathfrak{bms}_3$ algebra

Key Result

Theorem 2.1

CZZ Every local derivation on the Witt algebra $W$ is a derivation.

Theorems & Definitions (33)

  • Theorem 2.1
  • Corollary 2.2
  • proof
  • Lemma 2.3
  • Lemma 3.1
  • proof
  • Lemma 3.2
  • proof
  • Lemma 3.3
  • proof
  • ...and 23 more