Year: 1996
Type: preprint
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 $α\colon Γ\to \GL_n(\real)$ 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 $[G,G] \cap Γ$ (and $Γ$ is closed and $α$ is continuous).
Source: arXiv (Cornell University)
Author: Witte, Dave
Institution: Oklahoma State University
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2950224292