Some properties of the symmetric enveloping algebra of a subfactor, with applications to amenability and property \(T\)
type: Item
instance of: scholarly article
title: Some properties of the symmetric enveloping algebra of a subfactor, with applications to amenability and property \(T\)
zbMATH Open document ID: 0954.46037
published in: Documenta Mathematica
publication date: 2000-01-16T00:00:00Z
full work available at URL: https://eudml.org/doc/229322
full work available at URL: 20.html
review text: In order to gain more insight into the structure of subfactors \(N\subset M\) with finite Jones index, the author in [Math. Res. Lett. 1, No. 4, 409-425 (1994; Zbl 0902.46042)] introduced its symmetric enveloping algebra and the corresponding symmetric enveloping inclusion. In the present paper he undertakes a more detailed study of these objects, in particular, explores the question of amenability and property \(T\). For \(II_1\) factors it turns out that the symmetric enveloping algebra is amenable (i.e. hyperfinite) if and only if \(N\), \(M\), and the standard graph \(\Gamma_{N,M}\) are amenable. Moreover, as the main result he proves that amenability of subfactors is inherited by inclusions, thereby generalizing \textit{A. Connes}' hereditarity result for hyperfinite \(II_1\) factors [Ann. of Math., II. Ser. 104, 73-115 (1976; Zbl 0343.46042)].
Mathematics Subject Classification ID: 46L37
Mathematics Subject Classification ID: 46L80
zbMATH DE Number: 1388238
zbMATH Keywords: structure of subfactors
zbMATH Keywords: symmetric enveloping algebra
zbMATH Keywords: amenability
zbMATH Keywords: Jones index
author: Sorin Popa
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1388238