An exotic group as limit of finite special linear groups

Carderi, Alessandro; Thom, Andreas

Annales de l'Institut Fourier, Tome 68 (2018) no. 1, pp. 257-273.

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.

Classification : 54H11, 16E50, 43A07, 43A65
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.

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