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

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 [Citation1] 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 bms3 algebra.