On local Lie derivations of generalized matrix algebras

Abstract

Let $${\mathcal {G}}$$ be a generalized matrix algebra. We prove that, under certain conditions, every local Lie derivation $$\delta $$ of $${\mathcal {G}}$$ can be written in the form $$\delta =d+h$$, where d is a derivation of $${\mathcal {G}}$$ and h is a linear map from $${\mathcal {G}}$$ into $${\mathcal {Z}}({\mathcal {G}})$$ vanishing on each commutator. The result is then applied to some full matrix algebras and triangular algebras.