李群、局部紧群与射影李群的线性表示的核
Kernels of Linear Representations of Lie Groups, Locally Compact Groups, and Pro-Lie Groups
AI总结：
本文研究拓扑群常表示核的交集KO(G)，明确了连通李群、殆连通李群对应的KO类结构，证明连通射影李群的KO(G)含于其中心，并给出局部紧连通群下KO(G)的维数界及相关例子。
摘要：
针对拓扑群G，本文研究了所有常表示的核的交集KO(G)。我们证明，若G是连通射影李群，则KO(G)包含于G的中心。当C为连通李群类ConnLie或殆连通李群类almConnLie时，我们明确确定了KO(C)的结构：两种情况下，它均由所有紧生成阿贝尔李群构成。每个紧阿贝尔群和每个连通阿贝尔射影李群都可作为某个连通射影李群G的KO(G)。但当G是局部紧连通群时，KO(G)的维数以连续统的基数为上界。文中给出的例子表明，若C包含具有无限多个连通分支的群，KO(C)的结构会变得复杂。
英文摘要：
For a topological group G the intersection KO(G) of all kernels of ordinary representations is studied. We show that KO(G) is contained in the center of G if G is a connected pro-Lie group. The class KO(C) is determined explicitly if C is the class ConnLie of connected Lie groups or the class almConnLie of almost connected Lie groups: in both cases, it consists of all compactly generated abelian Lie groups. Every compact abelian group and every connected abelian pro-Lie group occurs as KO(G) for some connected pro-Lie group G. However, the dimension of KO(G) is bounded by the cardinality of the continuum if G is locally compact and connected. Examples are given to show that KO(C) becomes complicated if C contains groups with infinitely many connected components.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
