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- W2043312488 abstract "Je montre que le groupe linéaire GL(m, ℝ) contient un sous-groupe Zariski-dense dont tous les éléments n’ont que des valeurs propres positives si et seulement si m ≢ 2 modulo 4. Je généralise cet énoncé à tous les groupes algébriques réels. Je décris les adhérences de Zariski possibles pour les sous-groupes Γ de GL(m, ℝ) qui préservent un cône ouvert convexe saillant Ω de ℝm et dont l’action sur ℝm est irréductible. Je montre comment ces deux problèmes sont reliés. I show that the linear group GL(m, ℝ) contains a Zariski dense subgroup all of whose eigenvalues are positive if and only if m ≢ 2 modulo 4. I extend this statement to any real algebraic group. I describe the Zariski closure of the subgroups Γ of GL(m, ℝ) which preserve a properly convex open cone Ω of ℝm and whose action on ℝm is irreducible. I show how these two problems are related." @default.
- W2043312488 created "2016-06-24" @default.
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- W2043312488 date "1997-09-01" @default.
- W2043312488 modified "2023-09-30" @default.
- W2043312488 title "Groupes linéaires à valeurs propres positives et automorphismes des cônes convexes" @default.
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- W2043312488 doi "https://doi.org/10.1016/s0764-4442(97)88891-x" @default.
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