Bracket width of simple Lie algebras

Pub Date : 2021-02-17 DOI:10.4171/dm/850
A. Dubouloz, B. Kunyavskii, A. Regeta
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引用次数: 1

Abstract

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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单李代数的支架宽度
群的换向子宽度的概念,定义为表示派生群的每个元素作为它们的乘积所需的最小换向子数,在过去的几十年里得到了广泛的研究。特别地,1992年Barge和Ghys在光滑流形的微分同态群中发现了换向子宽度大于1的简单群的第一个例子。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。它们是在光滑仿射变异上多项式向量场的代数中发现的。
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