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TBDmathscidoc:1701.333172

Arkiv for Matematik, 48, (2), 311-321, 2008.6
In this note we establish some general finiteness results concerning lattices Γ in connected Lie groups$G$which possess certain “density” properties (see$Moskowitz$, M., On the density theorems of Borel and Furstenberg,$Ark. Mat.$$16(1978), 11–27, andMoskowitz, M., Some results on automorphisms of bounded displacement and bounded cocycles,Monatsh. Math.$$85$(1978), 323–336). For such groups we show that Γ always has finite index in its normalizer$N$_{$G$}(Γ). We then investigate analogous questions for the automorphism group Aut($G$) proving, under appropriate conditions, that Stab_{Aut($G$)}(Γ) is discrete. Finally we show, under appropriate conditions, that the subgroup $\tilde{\Gamma}=\{i_{\gamma}:\gamma \in \Gamma \},\ i_{\gamma}(x)=\gamma x\gamma^{-1}$ , of Aut($G$) has finite index in Stab_{Aut($G$)}(Γ). We test the limits of our results with various examples and counterexamples.
@inproceedings{frederick2008finiteness,
title={Finiteness results for lattices in certain Lie groups},
author={Frederick P. Greenleaf, and Martin Moskowitz},
url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203627626810981},
booktitle={Arkiv for Matematik},
volume={48},
number={2},
pages={311-321},
year={2008},
}

Frederick P. Greenleaf, and Martin Moskowitz. Finiteness results for lattices in certain Lie groups. 2008. Vol. 48. In Arkiv for Matematik. pp.311-321. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203627626810981.