Partial classification of the Baumslag-Solitar group von Neumann algebras
type: Item
instance of: scholarly article
title: Partial classification of the Baumslag-Solitar group von Neumann algebras
zbMATH Open document ID: 1314.46073
author: Niels Meesschaert
author: Stefaan Vaes
published in: Documenta Mathematica
publication date: 2014-10-20T00:00:00Z
full work available at URL: https://arxiv.org/abs/1301.0510
full work available at URL: 20.html
review text: Summary: We prove that the rational number \(|n/m|\) is an invariant of the group von Neumann algebra of the Baumslag-Solitar group \(\text{BS}(n,m)\). More precisely, if \(L(\text{BS}(n,m))\) is isomorphic with \(L(\text{BS}(n',m'))\), then \(|n'/m'| = |n/m|^{\pm 1}\). We obtain this result by associating to abelian, but not maximal abelian, subalgebras of a II\(_1\) factor, an equivalence relation that can be of type III. In particular, we associate to \(L(\text{BS}(n,m))\) a canonical equivalence relation of type III\(_{|n/m|}\).
Mathematics Subject Classification ID: 46L36
Mathematics Subject Classification ID: 20E06
Mathematics Subject Classification ID: 22D25
zbMATH DE Number: 6358805
zbMATH Keywords: invariant
zbMATH Keywords: group von Neumann algebras
zbMATH Keywords: Baumslag-Solitar group
MaRDI profile type: Publication
arXiv ID: 1301.0510
description: scientific article; zbMATH DE number 6358805