HIGHER GENERATION BY ABELIAN SUBGROUPS IN LIE GROUPS
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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.
Originalsprog | Engelsk |
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Tidsskrift | Transformation Groups |
Vol/bind | 28 |
Udgave nummer | 4 |
Sider (fra-til) | 1375–1390 |
Antal sider | 16 |
ISSN | 1083-4362 |
DOI | |
Status | Udgivet - 2023 |
ID: 276954540