HIGHER GENERATION BY ABELIAN SUBGROUPS IN LIE GROUPS
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HIGHER GENERATION BY ABELIAN SUBGROUPS IN LIE GROUPS. / Antolín-Camarena, O.; Gritschacher, S.; Villarreal, B.
In: Transformation Groups, Vol. 28, No. 4, 2023, p. 1375–1390.Research output: Contribution to journal › Journal article › Research › peer-review
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TY - JOUR
T1 - HIGHER GENERATION BY ABELIAN SUBGROUPS IN LIE GROUPS
AU - Antolín-Camarena, O.
AU - Gritschacher, S.
AU - Villarreal, B.
N1 - Publisher Copyright: © 2021, The Author(s).
PY - 2023
Y1 - 2023
N2 - 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.
AB - 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.
U2 - 10.1007/s00031-021-09659-8
DO - 10.1007/s00031-021-09659-8
M3 - Journal article
AN - SCOPUS:85107505906
VL - 28
SP - 1375
EP - 1390
JO - Transformation Groups
JF - Transformation Groups
SN - 1083-4362
IS - 4
ER -
ID: 276954540