Divisible convex sets. II. (Convexes divisibles. II.) (French) Zbl 1037.22022

Benoist, Yves

Duke Math. J. 120, No. 1, 97-120 (2003).

Summary: “A properly convex open cone in \(\mathbb{R}^m\) is called divisible if there exists a discrete subgroup \(\Gamma\) of \(\text{GL} (\mathbb{R}^m)\) preserving \(C\) such that the quotient \(\Gamma\setminus C\) is compact. We describe the Zariski closure of such a group \(\Gamma\). We show that if \(C\) is divisible but is neither a product nor a symmetric cone, then \(\Gamma\) is Zariski dense in \(\text{GL} (\mathbb{R}^m)\).” (Part I in C. R. Acad. Sci., Paris, Ser. I, Math. 332, 387–390 (2001; Zbl 1010.37014)].

MSC:

22E40	Discrete subgroups of Lie groups
20H15	Other geometric groups, including crystallographic groups
53A20	Projective differential geometry
57S30	Discontinuous groups of transformations

Citations:

Zbl 1010.37014

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