标题： $n$-Lie导子在广义矩阵代数上的表征 显示英文标题

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

摘要： 本文的主要目标是确定广义矩阵代数上的$n$-Lie导子（$n\geq 3$）的结构。在某些温和假设下，证明了每个$n$-Lie导子可以分解为一个极值$n$-导子和一个$n$-线性中心取值映射的和。作为直接应用，我们提供了全矩阵代数和三角代数上$n$-Lie导子的完整刻画。 显示英文摘要

摘要： 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.