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

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 [1] 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 ${\mathfrak{b}\mathfrak{m}\mathfrak{s}}_3$ algebra.

Keywords:

• Virasoro algebra
• local derivation
• $W(2,2)$
• deformed ${\mathfrak{b}\mathfrak{m}\mathfrak{s}}_3$ algebra

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work is partially supported by the NNSF [grant number 12071405], [grant number 11971315], [grant number 11871249].