Characterization of crossed product (properly infinite case)
type: Item
instance of: scholarly article
title: Characterization of crossed product (properly infinite case)
zbMATH Open document ID: 0693.46058
author: Hideki Kosaki
published in: Pacific Journal of Mathematics
publication date: 1989-01-01T00:00:00Z
review text: Let M be a properly infinite factor with a subfactor N and let E be a normal conditional expectation from M onto N with Index E\(=n\). Put \(N_ 1=IN'I\), where I is the modular conjugation on the standard \(L^ 2\)- space of M. The main result is the following theorem: If \(M\cap N^*=C_ 1\), \(M_ 1\cap N'\) is abelian, and \(\dim_ c(M_ 1\cap N')=n\), then there exist a finite group G (of order n) and an outer action \(\alpha\) of G on N such that M is the crossed product \(N\times_{\alpha}G\). (Furthermore, E is the canonical conditional expectation from \(N\times_{\alpha}G\) onto N).
Mathematics Subject Classification ID: 46L55
Mathematics Subject Classification ID: 46L35
zbMATH DE Number: 4134849
zbMATH Keywords: properly infinite factor
zbMATH Keywords: subfactor
zbMATH Keywords: normal conditional expectation
zbMATH Keywords: modular conjugation
zbMATH Keywords: crossed product
MaRDI profile type: Publication
full work available at URL: pjm.1989.137.159
OpenAlex ID: W2027539005
DOI: 10.2140/PJM.1989.137.159
description: scientific article; zbMATH DE number 4134849