On the existence of irreducible lattices
type: Item
instance of: scholarly article
title: On the existence of irreducible lattices
zbMATH Open document ID: 0563.22007
DOI: 10.1007/BF01193845
published in: Archiv der Mathematik
publication date: 1984-01-01T00:00:00Z
review text: Let G be a noncompact connected linear semisimple Lie group. A lattice in G is a discrete subgroup \(\Gamma\) with G/\(\Gamma\) of finite volume. If G has no compact factors, has a proper connected normal subgroup, and G/\(\Gamma\) is noncompact, Margulis and Ragunathan have given a necessary condition for \(\Gamma\) to be irreducible in G. The author sharpens this necessary condition to the condition that G must be \({\mathbb{Q}}\)-simple modulo compact factor and proves a converse under an extra hypothesis. This criterion is used to construct examples of irreducible lattices.
Mathematics Subject Classification ID: 22E40
zbMATH DE Number: 3897245
zbMATH Keywords: irreducibility
zbMATH Keywords: semisimple Lie group
zbMATH Keywords: lattice
author: F. E. A. Johnson
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3897245