Year: 2025
Type: article
Abstract: Subfactors of the hyperfinite II1 factor with “exotic” properties can be constructed from non-degenerate commuting squares of multi-matrix algebras. We show that the subfactor planar algebra of these commuting square subfactors necessarily embeds into Jones’ graph planar algebra associated to one of the inclusion graphs in the commuting square. This leads to a powerful obstruction for the standard invariant of the subfactor, and we use it to give an example of a hyperfinite subfactor with Temperley–Lieb–Jones standard invariant and index [Formula: see text], i.e. the index of the Haagerup subfactor. We are led to a conjecture pertaining to Jones indices of irreducible, hyperfinite subfactors.
Authors: Dietmar Bisch, Julio Cáceres
Institution: Vanderbilt University
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: Army Research Office
Awards: G7452299184, G828809702
OpenAlex ID: W4413837345