On the non-occurrence of the Coxeter graphs \(\beta_{2n+1}\), \(D_{2n+1}\) and \(E_ 7\) as the principal graph of an inclusion of II\(_ 1\) factors
type: Item
instance of: scholarly article
title: On the non-occurrence of the Coxeter graphs \(\beta_{2n+1}\), \(D_{2n+1}\) and \(E_ 7\) as the principal graph of an inclusion of II\(_ 1\) factors
zbMATH Open document ID: 0798.43005
author: V. S. Sunder
author: A. K. Vijayarajan
published in: Pacific Journal of Mathematics
publication date: 1994-04-27T00:00:00Z
review text: After discussing some preliminaries on the notion of an action of a hypergroup on a set, we present elementary proofs of the fact that the Coxeter graphs \(\beta_{2n+1}\), \(D_{2n+1}\) and \(E_ 7\) do not arise as Jones' principal graph invariant of an inclusion of \(\Pi_ 1\) factors. (Here, we use the symbol \(\beta_ n\) to denote the graph that is normally denoted by \(B_ n\), the reason for this changed terminology being spelt out in the text).
Mathematics Subject Classification ID: 43A62
Mathematics Subject Classification ID: 22D25
Mathematics Subject Classification ID: 46L35
zbMATH DE Number: 540681
zbMATH Keywords: hypergroup action
zbMATH Keywords: Coxeter graphs
zbMATH Keywords: Jones' principal graph invariant
zbMATH Keywords: \(\Pi_ 1\) factors
MaRDI profile type: Publication
full work available at URL: pjm.1993.161.185
OpenAlex ID: W2071224401
DOI: 10.2140/PJM.1993.161.185
description: scientific article; zbMATH DE number 540681