On the Topological Structure of Solvable Groups
On the Topological Structure of Solvable Groups
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可解群的拓扑结构
DOI：
10.2307/1969255
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发表时间：
1941
期刊：
影响因子：
--
通讯作者：
C. Chevalley
中科院分区：
文献类型：
--
作者：
C. Chevalley
E. Cartan证明了单连通可解李群与某个笛卡尔空间同胚。“我们想研究一个不一定是单连通的可解李群的结构。从一个著名的定理2可以得出这样一个群可以被认为是一个可解单连通群G通过G的中心的一个离散子群D的因子群。因此，我们要做的是在G组中寻找这样一个子组D的可能“情况”。
E. Cartan has shown that a simply connected solvable Lie group is homeomorphic to some Cartesian space.' We want to investigate the structure of a solvable Lie group which is not necessarily simply connected. From a well known theorem,2 it follows that such a group may be considered as the factor group of a solvable simply connected group G by a discrete subgroup D of the center of G. Therefore what we have to do is to look for the possible "situation" of such a sub-group D in the group G.