2024/10/18 by Dietmar Bisch, Bisch, Dietmar, Cáceres, Julio
Mathematics · #46L37 #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Geometric and Algebraic Topology #Operator Algebras (math.OA)
paper · pdf · doi:10.48550/arxiv.2410.14819
openalex publication_date 2024/10/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Subfactors of the hyperfinite II1 factor with ''exotic'' properties can be constructed from nondegenerate 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 (5+√(13))/(2), i.e. the index of the Haagerup subfactor. We are led to a conjecture pertaining to Jones indices of irreducible, hyperfinite subfactors.