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Restricted universal groups for right-angled buildings

Jens Bossaert and Tom De Medts (UGent)
(2023) INNOVATIONS IN INCIDENCE GEOMETRY. 20(2-3). p.177-208
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Abstract
Abstract In 2000, Marc Burger and Shahar Mozes introduced universal groups acting on trees. Such groups provide interesting examples of totally disconnected locally compact groups. Intuitively, these are the largest groups for which all local actions satisfy a prescribed behavior. Since then, their study has evolved in various directions. In particular, Adrien Le Boudec has studied restricted universal groups, where the prescribed behavior is allowed to be violated in a finite number of vertices. On the other hand, we have been studying universal groups acting on right-angled buildings, a class of geometric objects with a much more general structure than trees. The aim of the current paper is to combine both ideas: we will study restricted universal groups acting on right-angled buildings. We show several permutational and topological properties of those groups, with, as a main result, a precise criterion for when these groups are virtually simple.
Keywords
right-angled buildings, universal groups, locally compact groups, simple groups

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Citation

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MLA
Bossaert, Jens, and Tom De Medts. “Restricted Universal Groups for Right-Angled Buildings.” INNOVATIONS IN INCIDENCE GEOMETRY, vol. 20, no. 2–3, 2023, pp. 177–208, doi:10.2140/iig.2023.20.177.
APA
Bossaert, J., & De Medts, T. (2023). Restricted universal groups for right-angled buildings. INNOVATIONS IN INCIDENCE GEOMETRY, 20(2–3), 177–208. https://doi.org/10.2140/iig.2023.20.177
Chicago author-date
Bossaert, Jens, and Tom De Medts. 2023. “Restricted Universal Groups for Right-Angled Buildings.” INNOVATIONS IN INCIDENCE GEOMETRY 20 (2–3): 177–208. https://doi.org/10.2140/iig.2023.20.177.
Chicago author-date (all authors)
Bossaert, Jens, and Tom De Medts. 2023. “Restricted Universal Groups for Right-Angled Buildings.” INNOVATIONS IN INCIDENCE GEOMETRY 20 (2–3): 177–208. doi:10.2140/iig.2023.20.177.
Vancouver
1.
Bossaert J, De Medts T. Restricted universal groups for right-angled buildings. INNOVATIONS IN INCIDENCE GEOMETRY. 2023;20(2–3):177–208.
IEEE
[1]
J. Bossaert and T. De Medts, “Restricted universal groups for right-angled buildings,” INNOVATIONS IN INCIDENCE GEOMETRY, vol. 20, no. 2–3, pp. 177–208, 2023.
@article{01GSQ9XZ844NE1S4ZXEP0BJ7YC,
  abstract     = {{Abstract
In 2000, Marc Burger and Shahar Mozes introduced universal groups acting on trees. Such groups provide interesting examples of totally disconnected locally compact groups. Intuitively, these are the largest groups for which all local actions satisfy a prescribed behavior.
Since then, their study has evolved in various directions. In particular, Adrien Le Boudec has studied restricted universal groups, where the prescribed behavior is allowed to be violated in a finite number of vertices. On the other hand, we have been studying universal groups acting on right-angled buildings, a class of geometric objects with a much more general structure than trees.
The aim of the current paper is to combine both ideas: we will study restricted universal groups acting on right-angled buildings. We show several permutational and topological properties of those groups, with, as a main result, a precise criterion for when these groups are virtually simple.}},
  author       = {{Bossaert, Jens and De Medts, Tom}},
  issn         = {{2640-7337}},
  journal      = {{INNOVATIONS IN INCIDENCE GEOMETRY}},
  keywords     = {{right-angled buildings,universal groups,locally compact groups,simple groups}},
  language     = {{eng}},
  number       = {{2-3}},
  pages        = {{177--208}},
  title        = {{Restricted universal groups for right-angled buildings}},
  url          = {{http://doi.org/10.2140/iig.2023.20.177}},
  volume       = {{20}},
  year         = {{2023}},
}
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