2014/11/02 by Stephen Curran, Curran, S., Yoann Dabrowski +3
Mathematics · #46L37 #46L54 #Advanced Operator Algebra Research #FOS: Mathematics #Operator Algebras (math.OA) #Random Matrices and Applications #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.1411.0268
openalex publication_date 2014/11/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
We study 2-cabled analogs of Voiculescu's trace and free Gibbs states on Jones planar algebras. These states are traces on a tower of graded algebras associated to a Jones planar algebra. Among our results is that, with a suitable definition, finiteness of free Fisher information for planar algebra traces implies that the associated tower of von Neumann algebras consists of factors, and that the standard invariant of the associated inclusion is exactly the original planar algebra. We also give conditions that imply that the associated von Neumann algebras are non-Γ non-L2 rigid factors.