On flatness of Ocneanu's connections of the Dynkin diagrams and classification of subfactors
type: Item
instance of: scholarly article
title: On flatness of Ocneanu's connections of the Dynkin diagrams and classification of subfactors
zbMATH Open document ID: 0829.46048
author: Yasuyuki Kawahigashi
published in: Journal of Functional Analysis
publication date: 1996-01-22T00:00:00Z
review text: The author gives a proof of Ocneanu's announced classification of subfactors of the AFD type \(\text{II}_1\) factor with the principal graphs \(A_n\), \(D_n\), \(E_7\), the Dynkin diagrams, and gives a single explicit of \(\exp \pi\sqrt {-1}/ 24\) and \(\exp \pi\sqrt {-1}/ 60\) for each of \(E_6\) and \(E_8\) such that its validity is equivalent to the existence of two (and only two) subfactors for these principal graphs. His main tool is the flatness of connections on finite graphs, which is the key notion of Ocneanu's paragroup theory. He gives the difference between the diagrams \(D_{2n}\) and \(D_{2n+1}\) a meaning as a \(\mathbb{Z}/ 2\mathbb{Z}\)-obstruction for flatness arising in orbifold construction, which is an analogue of orbifold models in solvable lattice models.
Mathematics Subject Classification ID: 46L37
zbMATH DE Number: 763981
zbMATH Keywords: classification of subfactors
zbMATH Keywords: Dynkin diagrams
zbMATH Keywords: flatness of connections on finite graphs
zbMATH Keywords: Ocneanu's paragroup theory
zbMATH Keywords: orbifold construction
zbMATH Keywords: orbifold models
zbMATH Keywords: solvable lattice models
MaRDI profile type: Publication
full work available at URL: jfan.1995.1003
OpenAlex ID: W2073159852
DOI: 10.1006/JFAN.1995.1003
description: scientific article; zbMATH DE number 763981