Deformations of lattices in certain solvable groups
type: Item
instance of: scholarly article
title: Deformations of lattices in certain solvable groups
zbMATH Open document ID: 1144.22009
author: Cédric Rousseau
published in: Journal of the Mathematical Society of Japan
publication date: 2008-07-01T00:00:00Z
review text: Let \(G\) be a Lie subgroup of a Lie group \(H\). The author calls a subgroup \(\Gamma\) of \(G\) \(H\)-rigid if every small enough deformation of \(\Gamma\) in \(G\) is conjugate to \(\Gamma\) by an element of \(H\). Generalizing a theorem of A. Weil, he conjectures that this is the case for a finitely generated group \(\Gamma\) if the induced homomorphism \(H^1(\Gamma,\text{Ad}_G)\rightarrow H^1(\Gamma,\text{Ad}_H)\) in cohomology is zero. He confirms this for the case that \(\Gamma=\mathbb Z^n\rtimes_A\mathbb Z\), where \(n\geq 2\), \(A\) is a hyperbolic matrix in \(SL(n,\mathbb Z)\), and \(G=\mathbb R^n\rtimes_A\mathbb R\) is considered as a subgroup of \(H=SL(n+1,\mathbb R)\).
Mathematics Subject Classification ID: 22E40
Mathematics Subject Classification ID: 22E25
zbMATH DE Number: 5294950
zbMATH Keywords: local rigidity
zbMATH Keywords: lattices in solvable Lie groups
zbMATH Keywords: group cohomology
reviewed by: Herbert Abels
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2969/jmsj/06020397
OpenAlex ID: W1982603855
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DOI: 10.2969/JMSJ/06020397
description: scientific article; zbMATH DE number 5294950