2014/06/18 by Brent Nelson, Nelson, Brent · 1 citation
Mathematics · #46L37 #46L54 #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Operator Algebras (math.OA)
paper · pdf · doi:10.48550/arxiv.1406.4766
openalex publication_date 2014/06/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Given a finite depth subfactor planar algebra P endowed with the graded *-algebra structures \Grk+ P\k∈ℕ of Guionnet, Jones, and Shlyakhtenko, there is a sequence of canonical traces Trk,+ on Grk+P induced by the Temperley-Lieb diagrams and a sequence of trace-preserving embeddings into the bounded operators on a Hilbert space. Via these embeddings the *-algebras \Grk+P\k∈ ℕ generate a tower of non-commutative probability spaces \Mk,+\k∈ℕ whose inclusions recover P as its standard invariant. We show that traces Trk,+(v) induced by certain small perturbations of the Temperley-Lieb diagrams yield trace-preserving embeddings of Grk+P that generate the same tower \Mk,+\k∈ℕ.