On the nonoccurrence of the Coxeter graphs β_2n+1, D_2n+1 and E₇ as the principal graph of an inclusion of II₁ factors

Viakalathur Shankar Sunder and A. K. Vijayarajan

Vol. 161 (1993), No. 1, 185–200

DOI: 10.2140/pjm.1993.161.185

Abstract

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 β_2n+1, D_2n+1 and E₇ do not arise as Jones’ principal graph invariant of an inclusion of II₁ factors. (Here, we use the symbol β_n to denote the graph that is normally denoted by B_n, the reason for this changed terminology being spelt out in the text.)

Mathematical Subject Classification 2000

Primary: 46L37

Milestones

Received: 5 July 1991

Revised: 12 May 1992

Published: 1 November 1993