We prove a Kazhdan-Margulis-Zassenhaus lemma for Hilbert geometries. More precisely, in every dimension there exists a constant such that, for any properly convex open set and any point , any discrete group generated by a finite number of automorphisms of , which displace at a distance less than , is virtually nilpotent.
On montre un lemme de Kazhdan-Margulis-Zassenhaus pour les géométries de Hilbert. Plus précisément, en toute dimension , il existe une constante telle que, pour tout ouvert proprement convexe , pour tout point , tout groupe discret engendré par un nombre fini d’automorphismes de qui déplacent le point de moins de est virtuellement nilpotent.
Mot clés : Géométrie de Hilbert, lemme de Margulis, action géométriquement finie
Keywords: Hilbert’s geometry, lemma of Margulis, action geometrically finite
@article{AMBP_2013__20_2_363_0, author = {Crampon, Micka\"el and Marquis, Ludovic}, title = {Un lemme de {Kazhdan-Margulis-Zassenhaus} pour les g\'eom\'etries de {Hilbert}}, journal = {Annales math\'ematiques Blaise Pascal}, pages = {363--376}, publisher = {Annales math\'ematiques Blaise Pascal}, volume = {20}, number = {2}, year = {2013}, doi = {10.5802/ambp.330}, zbl = {1282.22007}, mrnumber = {3138033}, language = {fr}, url = {http://www.numdam.org/articles/10.5802/ambp.330/} }
TY - JOUR AU - Crampon, Mickaël AU - Marquis, Ludovic TI - Un lemme de Kazhdan-Margulis-Zassenhaus pour les géométries de Hilbert JO - Annales mathématiques Blaise Pascal PY - 2013 SP - 363 EP - 376 VL - 20 IS - 2 PB - Annales mathématiques Blaise Pascal UR - http://www.numdam.org/articles/10.5802/ambp.330/ DO - 10.5802/ambp.330 LA - fr ID - AMBP_2013__20_2_363_0 ER -
%0 Journal Article %A Crampon, Mickaël %A Marquis, Ludovic %T Un lemme de Kazhdan-Margulis-Zassenhaus pour les géométries de Hilbert %J Annales mathématiques Blaise Pascal %D 2013 %P 363-376 %V 20 %N 2 %I Annales mathématiques Blaise Pascal %U http://www.numdam.org/articles/10.5802/ambp.330/ %R 10.5802/ambp.330 %G fr %F AMBP_2013__20_2_363_0
Crampon, Mickaël; Marquis, Ludovic. Un lemme de Kazhdan-Margulis-Zassenhaus pour les géométries de Hilbert. Annales mathématiques Blaise Pascal, Volume 20 (2013) no. 2, pp. 363-376. doi : 10.5802/ambp.330. http://www.numdam.org/articles/10.5802/ambp.330/
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