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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Superrigid subgroups of solvable Lie groups
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by Dave Witte PDF
Proc. Amer. Math. Soc. 125 (1997), 3433-3438 Request permission


Let $\Gamma$ be a discrete subgroup of a simply connected, solvable Lie group $G$, such that $\operatorname {Ad}_G\Gamma$ has the same Zariski closure as $\operatorname {Ad} G$. If $\alpha \colon \Gamma \to \mathrm {GL}_n(\mathbb {R})$ is any finite-dimensional representation of $\Gamma$, we show that $\alpha$ virtually extends to a continuous representation $\sigma$ of $G$. Furthermore, the image of $\sigma$ is contained in the Zariski closure of the image of $\alpha$. When $\Gamma$ is not discrete, the same conclusions are true if we make the additional assumption that the closure of $[\Gamma , \Gamma ]$ is a finite-index subgroup of $[G,G] \cap \Gamma$ (and $\Gamma$ is closed and $\alpha$ is continuous).
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Additional Information
  • Dave Witte
  • Affiliation: Department of Mathematics, Oklahoma State University, Stillwater, Oklahoma 74078
  • Email:
  • Received by editor(s): June 21, 1996
  • Communicated by: Roe Goodman
  • © Copyright 1997 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 125 (1997), 3433-3438
  • MSC (1991): Primary 22E40; Secondary 22E25, 22E27, 22G05
  • DOI:
  • MathSciNet review: 1423339