[Un groupe exotique comme limite de groupes linéaires spéciaux finis]
Nous étudions un groupe polonais obtenu comme complétion de la limite inductive de groupes linéaires spéciaux finis munis de la distance induite par le rang. Ce groupe polonais est topologiquement simple modulo son centre, extrêmement moyennable et n’a pas de représentations fortement continues non triviales sur un espace de Hilbert.
We consider the Polish group obtained as the rank-completion of an inductive limit of finite special linear groups. This Polish group is topologically simple modulo its center, it is extremely amenable and has no non-trivial strongly continuous unitary representation on a Hilbert space.
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Keywords: Polish groups, von Neumann regular rings, extreme amenability and representation theory
Mot clés : groupes polonais, anneaux réguliers de von Neumann, moyennabilité extrême, théorie des représentations.
Carderi, Alessandro 1 ; Thom, Andreas 1
CC-BY-ND 4.0
@article{AIF_2018__68_1_257_0,
author = {Carderi, Alessandro and Thom, Andreas},
title = {An exotic group as limit of finite special linear groups},
journal = {Annales de l'Institut Fourier},
pages = {257--273},
publisher = {Association des Annales de l{\textquoteright}institut Fourier},
volume = {68},
number = {1},
year = {2018},
doi = {10.5802/aif.3160},
language = {en},
url = {https://aif.centre-mersenne.org/articles/10.5802/aif.3160/}
}
TY - JOUR AU - Carderi, Alessandro AU - Thom, Andreas TI - An exotic group as limit of finite special linear groups JO - Annales de l'Institut Fourier PY - 2018 SP - 257 EP - 273 VL - 68 IS - 1 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.3160/ DO - 10.5802/aif.3160 LA - en ID - AIF_2018__68_1_257_0 ER -
%0 Journal Article %A Carderi, Alessandro %A Thom, Andreas %T An exotic group as limit of finite special linear groups %J Annales de l'Institut Fourier %D 2018 %P 257-273 %V 68 %N 1 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.3160/ %R 10.5802/aif.3160 %G en %F AIF_2018__68_1_257_0
Carderi, Alessandro; Thom, Andreas. An exotic group as limit of finite special linear groups. Annales de l'Institut Fourier, Tome 68 (2018) no. 1, pp. 257-273. doi : 10.5802/aif.3160. https://aif.centre-mersenne.org/articles/10.5802/aif.3160/
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