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
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).
scientific article; zbMATH DE number 540681