两类幂零的n-Lie代数

Two Classes of Nilpotent n-Lie Algebras

本文提出并构造了两类幂零的n-Lie代数:特征幂零的n-Lie代数与最大秩的幂零的n-Lie代数.证明了n-Lie代数是特征幂零的n-Lie代数的充分必要条件,以及最大秩的幂零的n-Lie代数的结构特征.

In this paper, we propose two special classes of nilpotent n-Lie algebras which are characteristically nilpotent n-Lie algebras and nilpotent n-Lie algebras of maximal rank. We also give the characteristic structure on nilpotent n-Lie algebras of maximal rank and present the necessity and sufficiency on characteristically nilpotent n-Lie algebras.