Characterization of $n$-Lie Derivations on Generalized Matrix Algebras

TL;DR

This paper investigates the structure of higher-order Lie derivations on generalized matrix algebras, showing they can be decomposed into simpler components, with applications to matrix and triangular algebras.

Contribution

It provides a novel decomposition of $n$-Lie derivations on generalized matrix algebras, extending understanding of their structure under mild assumptions.

Findings

Decomposition of $n$-Lie derivations into extremal and centrally-valued parts

Complete characterization of $n$-Lie derivations on full matrix algebras

Complete characterization of $n$-Lie derivations on triangular algebras

Abstract

The principal objective of this paper is to determine the structure of $n$-Lie derivations ($n\geq 3$) on generalized matrix algebras.It is shown that under certain mild assumptions, every $n$-Lie derivation can be decomposed into the sum of an extremal $n$-derivation and an $n$-linear centrally-valued mapping. As direct applications, we provide complete characterizations of $n$-Lie derivations on both full matrix algebras and triangular algebras.