Locally normal subgroups and ends of locally compact Kac-Moody groups

Title: Locally normal subgroups and ends of locally compact Kac-Moody groups
Creator: Caprace, Pierre_Emmanuel; Marquis, Timothée; Reid, Colin D.
Relation: Münster Journal of Mathematics Vol. 15, p. 473-498
Publisher Link: http://dx.doi.org/10.17879/21089688074
Publisher: Westfaelische Wilhelms-Universitaet Muenster * Mathematisches Institut
Resource Type: journal article
Date: 2022
Description: 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.
Subject: subgroups; Kac_moody groups; assumptions; locally indecomposable
Identifier: http://hdl.handle.net/1959.13/1491457
Identifier: uon:53102
Identifier: ISSN:1867-5778
Language: eng
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