Analysis on discrete cocompact subgroups of the generic filiform Lie groups
type: Item
instance of: scholarly article
title: Analysis on discrete cocompact subgroups of the generic filiform Lie groups
zbMATH Open document ID: 1110.22004
author: Paul Milnes
author: Kamran Reihani
published in: Acta Mathematica Hungarica
publication date: 2007-01-08T00:00:00Z
review text: The standard filiform Lie group \({\mathcal F}_n\) contains a canonical lattice \({\mathcal D}_n\) given by integer coordinates. The current paper studies representations of the \(C^*\)-algebra \({\mathcal A}_n\) of \({\mathcal D}_n\). There are natural faithful representations on \(L^2\) of the \(n\)-dimensional torus, given by Anzai flows. There are also non-faithful representations which are given by matrix algebras over simple affine Furstenberg transformation groups \(C^*\) algebras of lower dimensional tori.
Mathematics Subject Classification ID: 22D25
Mathematics Subject Classification ID: 46L55
zbMATH DE Number: 5082282
zbMATH Keywords: filiform Lie group
zbMATH Keywords: discrete nilpotent group
zbMATH Keywords: group \(C^{\ast}\)-algebra
zbMATH Keywords: simple quotient
zbMATH Keywords: \(C^{\ast}\)-crossed product
Wikidata QID: Q115384341
reviewed by: Anton Deitmar
MaRDI profile type: Publication
full work available at URL: s10474-006-0059-z
OpenAlex ID: W1994253380
DOI: 10.1007/S10474-006-0059-Z
description: scientific article; zbMATH DE number 5082282