In this paper we study the minimal number of generators for simple Lie algebras in characteristic 0 or p > 3. We show that any such algebra can be generated by 2 elements. We also examine the 'one and a half generation' property, i.e. when every non-zero element can be completed to a generating pair. We show that classical simple algebras have this property, and that the only simple Cartan type algebras of type W which have this property are the Zassenhaus algebras.

在这篇文章中，我们研究了单李的最小生成元数目 特征为0或p>3的代数。我们证明了任何这样的代数都可以是 由2个元素生成。我们还考察了‘一代半’ 属性，即当每个非零元素都可以完成生成时 一对。我们证明了经典单代数具有这一性质，并且 只有具有这一性质的W型单Cartan型代数是 Zassenhaus代数。