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Topological and algebraic properties of universal groups for right-angled buildings

Jens Bossaert (UGent) and Tom De Medts (UGent)
(2021) FORUM MATHEMATICUM. 33(5). p.867-888
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Abstract
We study universal groups for right-angled buildings. Inspired by Simon Smith's work on universal groups for trees, we explicitly allow local groups that are not necessarily finite nor transitive. We discuss various topological and algebraic properties in this extended setting. In particular, we characterise when these groups are locally compact, when they are abstractly simple, when they act primitively on residues of the building, and we discuss some necessary and sufficient conditions for the groups to be compactly generated. We point out that there are unexpected aspects related to the geometry and the diagram of these buildings that influence the topological and algebraic properties of the corresponding universal groups.
Keywords
Right-angled buildings, universal groups, locally compact groups, simple, groups

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MLA
Bossaert, Jens, and Tom De Medts. “Topological and Algebraic Properties of Universal Groups for Right-Angled Buildings.” FORUM MATHEMATICUM, vol. 33, no. 5, 2021, pp. 867–88, doi:10.1515/forum-2020-0071.
APA
Bossaert, J., & De Medts, T. (2021). Topological and algebraic properties of universal groups for right-angled buildings. FORUM MATHEMATICUM, 33(5), 867–888. https://doi.org/10.1515/forum-2020-0071
Chicago author-date
Bossaert, Jens, and Tom De Medts. 2021. “Topological and Algebraic Properties of Universal Groups for Right-Angled Buildings.” FORUM MATHEMATICUM 33 (5): 867–88. https://doi.org/10.1515/forum-2020-0071.
Chicago author-date (all authors)
Bossaert, Jens, and Tom De Medts. 2021. “Topological and Algebraic Properties of Universal Groups for Right-Angled Buildings.” FORUM MATHEMATICUM 33 (5): 867–888. doi:10.1515/forum-2020-0071.
Vancouver
1.
Bossaert J, De Medts T. Topological and algebraic properties of universal groups for right-angled buildings. FORUM MATHEMATICUM. 2021;33(5):867–88.
IEEE
[1]
J. Bossaert and T. De Medts, “Topological and algebraic properties of universal groups for right-angled buildings,” FORUM MATHEMATICUM, vol. 33, no. 5, pp. 867–888, 2021.
@article{8724988,
  abstract     = {{We study universal groups for right-angled buildings. Inspired by Simon Smith's work on universal groups for trees, we explicitly allow local groups that are not necessarily finite nor transitive. We discuss various topological and algebraic properties in this extended setting. In particular, we characterise when these groups are locally compact, when they are abstractly simple, when they act primitively on residues of the building, and we discuss some necessary and sufficient conditions for the groups to be compactly generated. We point out that there are unexpected aspects related to the geometry and the diagram of these buildings that influence the topological and algebraic properties of the corresponding universal groups.}},
  author       = {{Bossaert, Jens and De Medts, Tom}},
  issn         = {{0933-7741}},
  journal      = {{FORUM MATHEMATICUM}},
  keywords     = {{Right-angled buildings,universal groups,locally compact groups,simple,groups}},
  language     = {{eng}},
  number       = {{5}},
  pages        = {{867--888}},
  title        = {{Topological and algebraic properties of universal groups for right-angled buildings}},
  url          = {{http://doi.org/10.1515/forum-2020-0071}},
  volume       = {{33}},
  year         = {{2021}},
}

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