Topologically Simple Infinite Matrix Groups Indexed by Ordered Sets
Journal of Lie Theory, Tome 35 (2025) no. 1, pp. 207-223
Voir la notice de l'article provenant de la source Heldermann Verlag
This article focusses on the study of the group of units of incidence rings, which is a class of infinite matrix groups indexed by ordered sets, in a topological perspective. We first show when these groups can inherit the topological structure from the incidence rings. It is later shown that infinite matrix groups of topological fields can be used to build simple topological matrix groups, generalizing a result proven recently by P. Groenhout, C. Reid and G. Willis [Topologically simple, totally disconnected, locally compact infinite matrix groups, J. Lie Theory 30 (2020) 965--980]. We finish by relating the structure of these groups with elementary totally disconnected, locally compact groups, an important class for the study of totally disconnected, locally compact groups.
Classification :
20G15, 20H25, 20E32, 06A06
Mots-clés : Infinite matrix groups, topological groups, simple topological groups
Mots-clés : Infinite matrix groups, topological groups, simple topological groups
Affiliations des auteurs :
João Vitor Pinto e Silva 1
João Vitor Pinto e Silva. Topologically Simple Infinite Matrix Groups Indexed by Ordered Sets. Journal of Lie Theory, Tome 35 (2025) no. 1, pp. 207-223. http://geodesic.mathdoc.fr/item/JOLT_2025_35_1_a10/
@article{JOLT_2025_35_1_a10,
author = {Jo\~ao Vitor Pinto e Silva},
title = {Topologically {Simple} {Infinite} {Matrix} {Groups} {Indexed} by {Ordered} {Sets}},
journal = {Journal of Lie Theory},
pages = {207--223},
year = {2025},
volume = {35},
number = {1},
url = {http://geodesic.mathdoc.fr/item/JOLT_2025_35_1_a10/}
}