- Author
- Pierre-Emmanuel Caprace and Tom De Medts (UGent)
- Organization
- Abstract
- We study closed subgroups G of the automorphism group of a locally finite tree T acting doubly transitively on the boundary. We show that if the stabiliser of some end is metabelian, then there is a local field k such that PSL2(k)≤G≤PGL2(k). We also show that the contraction group of some hyperbolic element is closed and torsion-free if and only if G is (virtually) a rank one simple p-adic analytic group for some prime p. A key point is that if some contraction group is closed, then G is boundary-Moufang, meaning that the boundary ∂T is a Moufang set. We collect basic results on Moufang sets arising at infinity of locally finite trees, and provide a complete classification in case the root groups are torsion-free.
- Keywords
- LIE-GROUPS, ROOT GROUPS, COMMENSURATORS, CLASSIFICATION, SUBGROUPS, LOCALLY COMPACT-GROUPS
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Citation
Please use this url to cite or link to this publication: http://hdl.handle.net/1854/LU-4344725
- MLA
- Caprace, Pierre-Emmanuel, and Tom De Medts. “Trees, Contraction Groups, and Moufang Sets.” DUKE MATHEMATICAL JOURNAL, vol. 162, no. 13, 2013, pp. 2413–49, doi:10.1215/00127094-2371640.
- APA
- Caprace, P.-E., & De Medts, T. (2013). Trees, contraction groups, and Moufang sets. DUKE MATHEMATICAL JOURNAL, 162(13), 2413–2449. https://doi.org/10.1215/00127094-2371640
- Chicago author-date
- Caprace, Pierre-Emmanuel, and Tom De Medts. 2013. “Trees, Contraction Groups, and Moufang Sets.” DUKE MATHEMATICAL JOURNAL 162 (13): 2413–49. https://doi.org/10.1215/00127094-2371640.
- Chicago author-date (all authors)
- Caprace, Pierre-Emmanuel, and Tom De Medts. 2013. “Trees, Contraction Groups, and Moufang Sets.” DUKE MATHEMATICAL JOURNAL 162 (13): 2413–2449. doi:10.1215/00127094-2371640.
- Vancouver
- 1.Caprace P-E, De Medts T. Trees, contraction groups, and Moufang sets. DUKE MATHEMATICAL JOURNAL. 2013;162(13):2413–49.
- IEEE
- [1]P.-E. Caprace and T. De Medts, “Trees, contraction groups, and Moufang sets,” DUKE MATHEMATICAL JOURNAL, vol. 162, no. 13, pp. 2413–2449, 2013.
@article{4344725,
abstract = {{We study closed subgroups G of the automorphism group of a locally finite tree T acting doubly transitively on the boundary. We show that if the stabiliser of some end is metabelian, then there is a local field k such that PSL2(k)≤G≤PGL2(k). We also show that the contraction group of some hyperbolic element is closed and torsion-free if and only if G is (virtually) a rank one simple p-adic analytic group for some prime p. A key point is that if some contraction group is closed, then G is boundary-Moufang, meaning that the boundary ∂T is a Moufang set. We collect basic results on Moufang sets arising at infinity of locally finite trees, and provide a complete classification in case the root groups are torsion-free.}},
author = {{Caprace, Pierre-Emmanuel and De Medts, Tom}},
issn = {{0012-7094}},
journal = {{DUKE MATHEMATICAL JOURNAL}},
keywords = {{LIE-GROUPS,ROOT GROUPS,COMMENSURATORS,CLASSIFICATION,SUBGROUPS,LOCALLY COMPACT-GROUPS}},
language = {{eng}},
number = {{13}},
pages = {{2413--2449}},
title = {{Trees, contraction groups, and Moufang sets}},
url = {{http://doi.org/10.1215/00127094-2371640}},
volume = {{162}},
year = {{2013}},
}
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