The first cohomology of parabolic actions for some higher-rank abelian groups and representation theory
type: Item
instance of: scholarly article
title: The first cohomology of parabolic actions for some higher-rank abelian groups and representation theory
zbMATH Open document ID: 1119.22009
author: David Mieczkowski
published in: Journal of Modern Dynamics
publication date: 2007-04-10T00:00:00Z
review text: From the introduction: ``In this article, we will compute the first smooth (or \(C^r\)) almost-cohomology \(H^1(A, L^2(G/\Gamma))\) for several examples of higher-rank parabolic abelian actions, and show that in some sense, the cohomology is as small as possible. In particular (with one notable exception) in each of our examples we show, for all irreducible unitary representations \(\pi\) of \(G\), that \(H^1_a(A, \pi)=0\). That is, all nontrivial obstructions to the cohomological equations vanish, and the first smooth (or \(C^r\)) almost-cohomology trivializes. Our method also works for some hyperbolic and mixed actions.''
reviewed by: Ioan Bucataru
Mathematics Subject Classification ID: 22E40
Mathematics Subject Classification ID: 37C85
Mathematics Subject Classification ID: 22E27
zbMATH DE Number: 5141225
zbMATH Keywords: first cohomology
zbMATH Keywords: parabolic actions
zbMATH Keywords: higher-rank abelian actions
zbMATH Keywords: representation theory
MaRDI profile type: Publication
full work available at URL: jmd.2007.1.61
OpenAlex ID: W2331951121
DOI: 10.3934/JMD.2007.1.61
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description: scientific article; zbMATH DE number 5141225