Finiteness results for lattices in certain Lie groups

Frederick P. Greenleaf, Martin Moskowitz

Research output: Contribution to journalArticle

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 - 2010

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Finiteness
Density Theorem
Normalizer
Analytic group
Cocycle
Automorphism Group
Counterexample
Automorphisms
Subgroup

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Finiteness results for lattices in certain Lie groups. / Greenleaf, Frederick P.; Moskowitz, Martin.

In: Arkiv for Matematik, Vol. 48, No. 2, 2010, p. 311-321.

Research output: Contribution to journalArticle

Greenleaf, Frederick P. ; Moskowitz, Martin. / Finiteness results for lattices in certain Lie groups. In: Arkiv for Matematik. 2010 ; Vol. 48, No. 2. pp. 311-321.
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