We call a finite, spanning set of a semi-simple real Lie algebra a distinguished set if it satisfies the following property: The Lie bracket of any two elements out of the set is, up to some constant, another element in the set; conversely, for any element in the set, there are two elements out of the set whose Lie bracket is, up to some constant, the given element. We show that every semi-simple real Lie algebra has a distinguished set.

中文翻译：

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半简单李代数的杰出集合

如果满足以下性质，我们将半简单实Lie代数的有限扩展集称为专有集：该集合中任意两个元素的Lie括号（在某种程度上来说是该集合中的另一个元素）；相反，对于集合中的任何元素，集合中有两个元素的李括号（在一定程度上）是给定元素。我们证明了每个半简单的实李代数都有一个杰出的集合。