Harmonic Analysis
Proper actions of lamplighter groups associated with free groups
Comptes Rendus. Mathématique, Volume 346 (2008) no. 3-4, pp. 173-176.

Given a finite group H and a free group Fn, we prove that the wreath product HFn admits a metrically proper, isometric action on a Hilbert space.

Soit H un groupe fini et F un groupe libre, ou plus généralement un groupe admettant une structure d'espace à murs invariante à gauche et propre. Nous montrons que le produit en couronne HF=H(F)F admet également une telle structure d'espace à murs. En conséquence, il a la propriété de Haagerup, c'est-à-dire qu'il possède une action isométrique métriquement propre sur un espace de Hilbert.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2007.11.027
de Cornulier, Yves 1; Stalder, Yves 2; Valette, Alain 3

1 Institut de recherche mathématique de Rennes, Université de Rennes 1, campus de Beaulieu, 35042 Rennes cedex, France
2 Laboratoire de mathématiques, Université Blaise-Pascal, campus universitaire des Cézeaux, 63177 Aubière cedex, France
3 Institut de mathématiques, Université de Neuchâtel, rue Émile-Argand 11, CP 158, CH-2009 Neuchâtel, Switzerland
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de Cornulier, Yves; Stalder, Yves; Valette, Alain. Proper actions of lamplighter groups associated with free groups. Comptes Rendus. Mathématique, Volume 346 (2008) no. 3-4, pp. 173-176. doi : 10.1016/j.crma.2007.11.027. http://www.numdam.org/articles/10.1016/j.crma.2007.11.027/

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Cited by Sources:

This research was performed at Centre Bernoulli (EPF Lausanne), in the framework of the semester “Limits of graphs in group theory and computer science”.