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1 October 2003 Convexes divisibles II
Yves Benoist
Duke Math. J. 120(1): 97-120 (1 October 2003). DOI: 10.1215/S0012-7094-03-12014-1

Abstract

Un cône ouvert proprement convexe C deℝm est dit divisible si il existe unsousgroupe discret Γ de GL(ℝm) quipréserve C et tel que quotient Γ\C est compact. Nous décrivons l'adhérence de Zariski d'un tel groupe Γ.

Nous montrons que si C n'est ni un produit ni un cône symétrique alors Γ est Zariski dense dans GL(ℝm).

A properly convex open cone in ℝm iscalled divisible if there exists a discrete subgroup Γ ofGLℝm preserving C such that thequotient Γ\C is compact. We describe the Zariski closure of such a group Γ.

We show that if C is divisible but is neither a product nor a symmetric cone, then Γ is Zariski dense in GLℝm.

Citation

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Yves Benoist. "Convexes divisibles II." Duke Math. J. 120 (1) 97 - 120, 1 October 2003. https://doi.org/10.1215/S0012-7094-03-12014-1

Information

Published: 1 October 2003
First available in Project Euclid: 16 April 2004

zbMATH: 1037.22022
MathSciNet: MR2010735
Digital Object Identifier: 10.1215/S0012-7094-03-12014-1

Subjects:
Primary: 22E40
Secondary: 20H15, 53A20, 57S30

Rights: Copyright © 2003 Duke University Press

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Vol.120 • No. 1 • 1 October 2003
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