A note on intermediate subfactors

Dietmar Bisch

Vol. 163 (1994), No. 2, 201–216

DOI: 10.2140/pjm.1994.163.201

Abstract

In this note we prove that if N ⊂ M ⊂ P is an inclusion of II₁ factors with finite Jones index such that N ⊂ P has finite depth, then N ⊂ M and M ⊂ P have finite depth. We show this result by studying the iterated basic constructions for M ⊂ P and N ⊂ P. In particular our proof gives detailed information about the graphs for N ⊂ M resp. M ⊂ P. Furthermore, we give an abstract characterization of intermediate subfactors in terms of Jones projections in N′∩ P₁, where N ⊂ P ⊂ P₁ is the basic construction for N ⊂ P and give examples showing that if N ⊂ M and M ⊂ P have finite depth, then N ⊂ P does not necessarily have finite depth.

Mathematical Subject Classification 2000

Primary: 46L37

Milestones

Received: 15 April 1992

Revised: 16 August 1992

Published: 1 April 1994