2009/06/23 by David Evans, David E. Evans, Evans, David E. +2
Mathematics · Physics and Astronomy · #46L37 (Primary) #46L60 #81T40 (Secondary) #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Operator Algebras (math.OA) #Quantum Algebra (math.QA) #hep-th #math-ph #math.MP #math.OA #math.QA #msc:46L37 #msc:46L60 #msc:81T40
paper · pdf · doi:10.48550/arxiv.0906.4311
33 pages, 19 figures; revised definition of A_2-planar modules, improvements to exposition and introduction
openalex publication_date 2009/06/23 · arxiv created 2011/05/27 · arxiv updated 2011/05/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Generalizing Jones's notion of a planar algebra, we have previously introduced an A2-planar algebra capturing the structure contained in the double complex pertaining to the subfactor for a finite SU(3) ADE graph with a flat cell system. We now introduce the notion of modules over an A2-planar algebra, and describe certain irreducible Hilbert A2-TL-modules. We construct an A2-graph planar algebra associated to each pair (G,W) given by an SU(3) ADE graph G and a cell system W on G. A partial modular decomposition of these A2-graph planar algebras is achieved.