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February, 2002 On the Zariski Closure of the Linear Part of a Properly Discontinuous Group of Affine Transformations
H. Abels, G.A. Margulis, G.A. Soifer
J. Differential Geom. 60(2): 315-344 (February, 2002). DOI: 10.4310/jdg/1090351104

Abstract

Let $\Gamma$ be a subgroup of the group of affine transformations of the affine space $\mathbb{R}^{2n+1}$. Suppose $\Gamma$ acts properly discontinuously on $\mathbb{R}^{2n+1}$. The paper deals with the question which subgroups of $\rm{GL}(2n +1,\mathbb{R})$ occur as Zariski closure $\overline{\ell (\Gamma})$ of the linear part of such a group $\Gamma$. The two main results of the paper say that $\rm{SO}(n + 1, n)$ does occur as $\overline{\ell (\Gamma)}$ of such a group$\Gamma$ if $n$ is odd, but does not if $n$ is even.

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H. Abels. G.A. Margulis. G.A. Soifer. "On the Zariski Closure of the Linear Part of a Properly Discontinuous Group of Affine Transformations." J. Differential Geom. 60 (2) 315 - 344, February, 2002. https://doi.org/10.4310/jdg/1090351104

Information

Published: February, 2002
First available in Project Euclid: 20 July 2004

zbMATH: 1061.22012
MathSciNet: MR1938115
Digital Object Identifier: 10.4310/jdg/1090351104

Rights: Copyright © 2002 Lehigh University

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Vol.60 • No. 2 • February, 2002
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