Locally normal subgroups and ends of locally compact Kac–Moody groups
(2022) Muenster Journal of Mathematics — Vol. 15, n° 2, p. 473-498 (2022)
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- Abstract
- A locally normal subgroup in a topological group is a subgroup whose normaliser 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 [Caprace-Marquis-Reid, Growing trees from compact subgroups], we show that under mild assumptions, if the Kac-Moody group is one-ended (a property that is easily determined from the generalised Cartan matrix), then it is locally indecomposable, which means that no open subgroup decomposes as a nontrivial direct product.
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Caprace, P.-E., Marquis, T., & Reid, D. C. (2022). Locally normal subgroups and ends of locally compact Kac–Moody groups. Muenster Journal of Mathematics, 15(2), 473-498. https://doi.org/10.17879/21089688074 (Original work published 2022)