单李代数的宽度
Bracket width of simple Lie algebras
摘要：
群的换位子宽度的概念，定义为将导出群的每个元素表示为它们的乘积所需的换位子的最小数目，在过去的几十年中得到了广泛的研究。特别是，在1992年巴奇和Ghys发现了第一个例子，一个简单的一组交换子宽度大于一组之间的同构的光滑流形。我们考虑了李代数的括号宽度的平行概念，并给出了括号宽度大于1的简单李代数的第一个例子。它们存在于光滑仿射簇上的多项式向量场的代数中。
英文摘要：
The notion of commutator width of a group, defined as the smallest number of commutators needed to represent each element of the derived group as their product, has been extensively studied over the past decades. In particular, in 1992 Barge and Ghys discovered the first example of a simple group of commutator width greater than one among groups of diffeomorphisms of smooth manifolds. We consider a parallel notion of bracket width of a Lie algebra and present the first examples of simple Lie algebras of bracket width greater than one. They are found among the algebras of polynomial vector fields on smooth affine varieties.
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