Finiteness results for lattices in certain Lie groups

Frederick P. Greenleaf, Martin Moskowitz

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Abstract

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, and Moskowitz, 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 NG(Γ). We then investigate analogous questions for the automorphism group Aut(G) proving, under appropriate conditions, that StabAut(G)(Γ) is discrete. Finally we show, under appropriate conditions, that the subgroup, of Aut(G) has finite index in StabAut(G)(Γ). We test the limits of our results with various examples and counterexamples.

Original languageEnglish (US)
Pages (from-to)311-321
Number of pages11
JournalArkiv for Matematik
Volume48
Issue number2
DOIs
StatePublished - Jan 1 2010

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ASJC Scopus subject areas

  • Mathematics(all)

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