T-property and nonisomorphic full factors of types II and III
type: Item
instance of: scholarly article
title: T-property and nonisomorphic full factors of types II and III
zbMATH Open document ID: 0614.46053
DOI: 10.1016/0022-1236(87)90123-6
author: N. I. Nessonov
author: V. Ya. Golodets
published in: Journal of Functional Analysis
publication date: 1987-01-01T00:00:00Z
review text: The paper deals with the actions of T-groups on von Neumann hyperfinite algebras. It is proved that there exist factors of type II with various countable fundamental groups and hence various actions. The results obtained are used to prove the existence of nonisomorphic full factors of type III\(_ 1\) with a fixed Connes invariant Sd. Here are two of the results proved in the paper. 1. For any given countable subgroup \(\Gamma \subset {\mathbb{R}}^*_+\) there exists a factor \(M\) of type II with the countable fundamental group \(F(M)\), so that F(M)\(\supset \Gamma.\) 2. Any T(ICC)-group has a continuum of nonequivalent actions onto hyperfinite factors of type II.
Mathematics Subject Classification ID: 46L35
Mathematics Subject Classification ID: 46L55
zbMATH DE Number: 3994311
zbMATH Keywords: T-property
zbMATH Keywords: actions of T-groups on von Neumann hyperfinite algebras
zbMATH Keywords: factors of type II
zbMATH Keywords: existence of nonisomorphic full factors
zbMATH Keywords: Connes invariant
zbMATH Keywords: countable subgroup
zbMATH Keywords: countable fundamental group
zbMATH Keywords: continuum of nonequivalent actions
MaRDI profile type: Publication
full work available at URL: 0022-1236(87)90123-6
OpenAlex ID: W2043594297
cites work: Q3903544
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cites work: A non-commutative extension of abstract integration
cites work: Almost periodic states and factors of type III\(_1\)
cites work: Hyperfinite and \(II_ 1 \)actions for nonamenable groups
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description: scientific article; zbMATH DE number 3994311