HIGHER GENERATION BY ABELIAN SUBGROUPS IN LIE GROUPS

被引：0
作者：
O. ANTOLÍN-CAMARENA
S. GRITSCHACHER
B. VILLARREAL
机构：
[1] Ciudad Universitaria,Instituto de Matemáticas, UNAM
[2] University of Copenhagen,Department of Mathematical Sciences
来源：
Transformation Groups | 2023年 / 28卷
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摘要：
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 πi(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.
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页码：1375 / 1390
页数：15
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