论文标题
阿贝里亚亚组的较高一代在谎言组中
Higher generation by abelian subgroups in Lie groups
论文作者
论文摘要
对于一个紧凑的谎言组$ g $，一个人可以将空间$ e（2，g）与离散组的阿贝尔亚群的coset相似。 Space $ e（2，g）$由Adem，F。Cohen和Torres-Giese介绍，随后由Adem和Gómez以及其他作者进行了研究。在此简短说明中，我们证明$ g $是Abelian，并且仅当$π_i（e（e（2，g））= 0 $ for $ i = 1,2,4 $时。这是一个谎言群体的类似物，即一个事实，即离散群体的阿贝尔亚群体的coset是简单地与之相关的，并且仅当该群体是Abelian时。
To a compact Lie group $G$ one can associate a space $E(2,G)$ akin to the poset of cosets of abelian subgroups of a discrete group. The space $E(2,G)$ was introduced by Adem, F. Cohen and Torres-Giese, and subsequently studied by Adem and Gómez, and other authors. In this short note, we prove that $G$ is abelian if and only if $π_i(E(2,G))=0$ for $i=1,2,4$. This is a Lie group analogue of the fact that the poset of cosets of abelian subgroups of a discrete group is simply--connected if and only if the group is abelian.
