关于n-李代数导子的一个注记

A Note on Derivations of n-Lie Algebras

借助于n-李代数对导子的根子空间直和分解以及它的正则表示的研究,得出具有一个特征根均为正实数的导子的n-李代数是幂零的,从而用导子刻画了n-李代数的幂零性.

By means of studying the direct sum of root subspaces about derivation of an n-Lie algebra and regular representations of n-Lie algebras,we show that a n-Lie algebra admitting a derivation with all characteristic roots being positive real number must be nilpotent.So we can determinate the nilpotence of n-Lie algebras by the properties of derivation.