HIGHER GENERATION BY ABELIAN SUBGROUPS IN LIE GROUPS

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Standard

HIGHER GENERATION BY ABELIAN SUBGROUPS IN LIE GROUPS. / Antolín-Camarena, O.; Gritschacher, S.; Villarreal, B.

I: Transformation Groups, Bind 28, Nr. 4, 2023, s. 1375–1390.

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt

Harvard

Antolín-Camarena, O, Gritschacher, S & Villarreal, B 2023, 'HIGHER GENERATION BY ABELIAN SUBGROUPS IN LIE GROUPS', Transformation Groups, bind 28, nr. 4, s. 1375–1390. https://doi.org/10.1007/s00031-021-09659-8

APA

Antolín-Camarena, O., Gritschacher, S., & Villarreal, B. (2023). HIGHER GENERATION BY ABELIAN SUBGROUPS IN LIE GROUPS. Transformation Groups, 28(4), 1375–1390. https://doi.org/10.1007/s00031-021-09659-8

Vancouver

Antolín-Camarena O, Gritschacher S, Villarreal B. HIGHER GENERATION BY ABELIAN SUBGROUPS IN LIE GROUPS. Transformation Groups. 2023;28(4):1375–1390. https://doi.org/10.1007/s00031-021-09659-8

Author

Antolín-Camarena, O. ; Gritschacher, S. ; Villarreal, B. / HIGHER GENERATION BY ABELIAN SUBGROUPS IN LIE GROUPS. I: Transformation Groups. 2023 ; Bind 28, Nr. 4. s. 1375–1390.

Bibtex

@article{56ddf9e6f0cf44ad8e4a90874f9efaed,
title = "HIGHER GENERATION BY ABELIAN SUBGROUPS IN LIE GROUPS",
abstract = "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 G{\'o}mez, 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.",
author = "O. Antol{\'i}n-Camarena and S. Gritschacher and B. Villarreal",
note = "Publisher Copyright: {\textcopyright} 2021, The Author(s).",
year = "2023",
doi = "10.1007/s00031-021-09659-8",
language = "English",
volume = "28",
pages = "1375–1390",
journal = "Transformation Groups",
issn = "1083-4362",
publisher = "Springer Basel AG",
number = "4",

}

RIS

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