The Annular Structure of Subfactors

2001/05/09 by Vaughan F. R. Jones, Jones, Vaughan F. R. · 1 citation
Chemistry · Mathematics · #46L37 #57M25 #FOS: Mathematics #Inorganic Fluorides and Related Compounds #Operator Algebras (math.OA) #Quantum Algebra (math.QA) #math.OA #math.QA #msc:46L37 #msc:57M25

paper · pdf · doi:10.48550/arxiv.math/0105071

62 pages, includes 2 tables and 24 figures, to be published in L'Enseignement Mathematique

arxiv created 2001/05/09 · openalex publication_date 2001/05/09 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Given a planar algebra we show the equivalence of the notions of a module over this algebra (in the operadic sense), and module over a universal annular algebra. We classify such modules, with invariant inner products, in the generic region and give applications to subfactorss, including a planar construction of the E₆ and E₈ subfactors.

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