Locally normal subgroups and ends of locally compact Kac–Moody groups
A locally normal subgroup in a topological group is a subgroup whose normalizer is open. In this paper, we provide a detailed description of the large-scale structure of closed locally normal subgroups of complete Kac–Moody groups over finite fields. Combining that description with the main result f...
| Verfasser: | |
|---|---|
| Dokumenttypen: | Artikel |
| Medientypen: | Text |
| Erscheinungsdatum: | 2022 |
| Publikation in MIAMI: | 26.01.2023 |
| Datum der letzten Änderung: | 26.01.2023 |
| Quelle: | Münster Journal of Mathematics, 15 (2022), S. 473-498 |
| Verlag/Hrsg.: |
Mathematisches Institut (Universität Münster)
|
| Angaben zur Ausgabe: | [Electronic ed.] |
| Fachgebiet (DDC): | 510: Mathematik |
| Lizenz: | InC 1.0 |
| Sprache: | Englisch |
| Format: | PDF-Dokument |
| URN: | urn:nbn:de:hbz:6-21089688412 |
| Weitere Identifikatoren: | DOI: 10.17879/21089688074 |
| Permalink: | https://nbn-resolving.de/urn:nbn:de:hbz:6-21089688412 |
| Onlinezugriff: | mjm_2022_15_473-498.pdf |
A locally normal subgroup in a topological group is a subgroup whose normalizer is open. In this paper, we provide a detailed description of the large-scale structure of closed locally normal subgroups of complete Kac–Moody groups over finite fields. Combining that description with the main result from [7], we show that, under mild assumptions, if the Kac–Moody group is one-ended (a property that is easily determined from the generalized Cartan matrix), then it is locally indecomposable, which means that no open subgroup decomposes as a nontrivial direct product.