Generalized Lie n-derivations of triangular algebras

Abstract

Abstract Let be a triangular algebra. We show that under suitable assumptions every generalized Lie n-derivation associated with a linear map is of the form where and Δ is a Lie n-derivation of We solve this problem using commuting and centralizing maps. We also prove that under certain mild conditions any centralizing map on a triangular algebra is commuting. As an application, we give a description of generalized Lie n-derivations on classical examples of triangular algebras: upper triangular matrix algebras and nest algebras.