Superrigid subgroups of solvable Lie groups

1996/07/01 by Dave Witte, Witte, Dave
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT) #math.RT

paper · pdf · doi:10.48550/arxiv.math/9607221

arxiv created 1996/07/01 · openalex publication_date 1996/07/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let Γ be a discrete subgroup of a simply connected, solvable Lie group~G, such that \Ad_GΓ has the same Zariski closure as \Ad G. If α\colon Γ→ \GL_n(\real) 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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