Index for factors generated by Jones’ two sided sequence of projections

Marie Choda

Vol. 139 (1989), No. 1, 1–16

DOI: 10.2140/pjm.1989.139.1

Abstract

Let {e_i;i = 0,±1,±2,…} be a family of projections with the property; (a) e_ie_i±1e_i = λe_i for some λ ≤ 1, (b) e_ie_j = e_je_i for |i − j|≥ 2, (c) the von Neumann algebra M generated by the family {e_i;i = 0,±1,±2,…} is a hyperfinite II₁-factor with the trace tr and (d) tr(we_i) = λ tr(w) if w is a word on 1 and e_j(j ≤ i − 1). Let N be a von Neumann algebra generated by {e_i;i = ±1,±2,…}. Then N is a subfactor of M. If λ = (1∕4)sec²(π∕m) for some integer m (m ≥ 3), then N′∩M = C1 and the index [M : N] = (m∕4)cosec²(π∕m).

Mathematical Subject Classification 2000

Primary: 46L35

Secondary: 46L37

Milestones

Received: 10 October 1987

Revised: 4 July 1988

Published: 1 September 1989