Generalized Lie n-derivations on generalized matrix algebras

Abstract

Let $ \mathcal{G} $ be a generalized matrix algebra. We show that under certain conditions, each generalized Lie $ n $-derivation associated with a linear map on $ \mathcal{G} $ is a sum of a generalized derivation and a central map vanishing on all $ (n-1) $-th commutators and is also a sum of a generalized inner derivation and a Lie $ n $-derivation. As an application, generalized Lie $ n $-derivations on von Neumann algebras are characterized.

Keywords

• generalized lie $ n $-derivation
• lie $ n $-derivation
• generalized matrix algebra