(untitled) (Contemporary Mathematics, 2025)
Local derivation is a significant concept for various algebras, which measures some kind of local property of the algebras. This paper aims to study the local derivations on the planar Galilean conformal algebra. We determine all local derivations on the planar Galilean conformal algebra. Unlike the case of the Virasoro algebra and W(2, 2), there indeed exists a nontrivial local derivation on the planar Galilean conformal algebra. The key construction and some methods will help to do such researches for some other Lie (super)algebras.