Multiplicative Lie n-derivations of triangular rings

AbstractWe introduce the notion of a multiplicative Lie n-derivation of a ring, generalizing the notion of a Lie (triple) derivation. The main goal of the paper is to consider the question of when do all multiplicative Lie n-derivations of a triangular ring T have the so-called standard form. The main result is applied to the classical examples of triangular rings: nest algebras and (block) upper triangular matrix rings