An exotic group as limit of finite special linear groups
Annales de l'Institut Fourier, Volume 68 (2018) no. 1, pp. 257-273.

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.

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.

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DOI: 10.5802/aif.3160
Classification: 54H11,  16E50,  43A07,  43A65
Keywords: Polish groups, von Neumann regular rings, extreme amenability and representation theory
Carderi, Alessandro 1; Thom, Andreas 1

1 Institut für Geometrie TU Dresden 01062 Dresden (Germany)
License: CC-BY-ND 4.0
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Carderi, Alessandro; Thom, Andreas. An exotic group as limit of finite special linear groups. Annales de l'Institut Fourier, Volume 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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