Superrigid Subgroups of Solvable Lie Groups
نویسنده
چکیده
Let Γ be a discrete subgroup of a simply connected, solvable Lie group G, such that AdG Γ has the same Zariski closure as AdG. If α : Γ → GLn(R) is any finite-dimensional representation of Γ, we show that α virtually extends to a continuous representation σ of G. Furthermore, the image of σ is contained in the Zariski closure of the image of α. When Γ is not discrete, the same conclusions are true if we make the additional assumption that the closure of [Γ,Γ] is a finite-index subgroup of [G,G] ∩ Γ (and Γ is closed and α is continuous).
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