2004/12/21 by Pinhas Grossman, Grossman, Pinhas, Vaughan F. R. Jones +1
Mathematics · #46L37 #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Operator Algebras (math.OA) #math.OA #msc:46L37
paper · pdf · doi:10.48550/arxiv.math/0412423
51 pages, 65 figures
openalex publication_date 2004/12/21 · arxiv created 2005/02/14 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
If N ⊂ P,Q ⊂ M are type II1 factors with N' ∩ M = C id and [M:N] finite we show that restrictions on the standard invariants of the elementary inclusions N ⊂ P, N ⊂ Q, P ⊂ M and Q ⊂ M imply drastic restrictions on the indices and angles between the subfactors. In particular we show that if these standard invariants are trivial and the conditional expectations onto P and Q do not commute, then [M:N] is 6 or 6 + 4√ 2. In the former case N is the fixed point algebra for an outer action of S3 on M and the angle is π/3, and in the latter case the angle is cos-1(√ 2-1) and an example may be found in the GHJ subfactor family. The techniques of proof rely heavily on planar algebras.