On Discrete Subgroups of Lie Groups (II)
On Discrete Subgroups of Lie Groups (II)
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关于李群的离散子群（二）
DOI：
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发表时间：
1962
期刊：
影响因子：
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通讯作者：
A. Weil
中科院分区：
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作者：
A. Weil
1.这是我的论文[7]的延续，标题相同，将被称为D '，并且必须以附录I中描述的方式进行补充。事实上，本文件只不过是一个相结合的想法D'的方法变化的结构，适用于特殊类型的半单群的卡拉比和卡拉比-Vesentini在他们最近的工作。我们将主要关注没有紧分支的半单群，即，连通半单李群没有连通紧正规子群。然而，我们开始考虑任何连通李群G至少有一个离散子群具有紧商;这意味着G是幺模的（甚至可以假设G有一个离散子群H，使得G/H有一个有限测度，对于G/H上的测度由G上的右不变测度确定）。设n是G的维数;为G上的右不变向量场空间选择一个基X1，*，Xn;我们有
1. This is a continuation of my paper [7] with the same title, which will be referred to as D', and which has to be supplemented in the manner described below in Appendix I. Indeed, the present paper is nothing else than a combination of the ideas of D' with the method of variation of structure, as applied to special types of semisimple groups by Calabi and by Calabi-Vesentini in their recent work'. We shall mainly be concerned with semisimple groups without compact components, i.e., with connected semisimple Lie groups having no connected compact normal subgroup. However, we begin by considering any connected Lie group G having at least one discrete subgroup with compact quotient; this implies that G is unimodular (it would even be enough for this to assume that G has a discrete subgroup H such that G/H has a finite measure, for the measure determined on G/Hby a right-invariant measure on G). Let n be the dimension of G; choose a basis X1, * , Xn for the space of right-invariant vector-fields on G; we have