Un lemme de Kazhdan-Margulis-Zassenhaus pour les géométries de Hilbert

Mickaël Crampon; Ludovic Marquis

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arXiv · 1106.3156

Un lemme de Kazhdan-Margulis-Zassenhaus pour les géométries de Hilbert

Mickaël Crampon·Ludovic Marquis

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Abstract

We prove a Kazhdan-Margulis-Zassenhaus lemma for Hilbert geometries. More precisely, in every dimension $n$ there exists a constant $\varepsilon_n > 0$ such that, for any properly open convex set $Ø$ and any point $x \in Ø$, any discrete group generated by a finite number of automorphisms of $Ø$, which displace $x$ at a distance less than $\varepsilon_n$, is virtually nilpotent.

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BibTeX RIS

Mickaël Crampon, Ludovic Marquis. 2013-02-11. Un lemme de Kazhdan-Margulis-Zassenhaus pour les géométries de Hilbert. https://arxiv.org/abs/1106.3156

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