On commuting squares and subfactors
type: Item
instance of: scholarly article
title: On commuting squares and subfactors
zbMATH Open document ID: 0739.46042
DOI: 10.1016/0022-1236(91)90159-3
author: V. S. Sunder
published in: Journal of Functional Analysis
publication date: 1992-06-27T00:00:00Z
review text: An explicit construction of irreducible selfdual subfactors of the hyperfinite factor \(R\) by using a certain type of commuting squares of matrix algebras are presented. Examples so constructed give some information about the set \(I^ 0_ R\) of index values of irreducible (selfdual) subfactors of \(R\) and its derived sets: \({\mathcal D}^ N(I^ 0_ R)=\) the set of all accumulation points of \({\mathcal D}^{N-1}(I^ 0_ R)\) \((N=1,2,\ldots)\). For example, for any positive integer \(N\), \((N+(N^ 2+4)^{1/2})/2\), \((N+(N^ 2+8)^{1/2})/2\in I^ 0_ R\), \((N+N^{-1})^ 2\in{\mathcal D}(I^ 0_ R)\), \((N+1)^ 2\in{\mathcal D}^ N(I^ 0_ R)\). The construction is based on the matrix \[ L= \left[\begin{matrix} 0 &1 &0 &\ldots && 0 \\ 1 &N_ 2 &1 &\ldots &&0 \\ 0 &1 &N_ 3 &\ldots &&0 \\ \vdots &\vdots &\vdots &&&\vdots \\ 0 &. &. &.1 &N_{n-1} &1 \\ 0 &. &. &.0 &1 &N_ n \end{matrix} \right], \] where \(N_ 2,N_ 3, \ldots, N_ n\) are non-decreasing sequences of non-negative integers. \(\| L\|^ 2\) gives the index.
Mathematics Subject Classification ID: 46L37
Mathematics Subject Classification ID: 46L35
zbMATH DE Number: 25998
zbMATH Keywords: times tunnel
zbMATH Keywords: explicit construction of irreducible selfdual subfactors of the hyperfinite factor
zbMATH Keywords: commuting squares of matrix algebras
zbMATH Keywords: index values
zbMATH Keywords: accumulation points
reviewed by: Huzihiro Araki
MaRDI profile type: Publication
full work available at URL: 0022-1236(91)90159-3
OpenAlex ID: W2009087549
cites work: Q4693152
cites work: Index for subfactors
cites work: Q3472677
cites work: Entropy and index for subfactors
cites work: Q3468159
cites work: Q4284561
cites work: Hecke algebras of type \(A_ n\) and subfactors
description: scientific article; zbMATH DE number 25998