Skein theory for the ADE planar algebras

2009/03/01 by Stephen Bigelow, Bigelow, Stephen
Mathematics · #46L37 #46M99 #57M15 #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Operator Algebras (math.OA) #Quantum Algebra (math.QA) #math.OA #math.QA #msc:46L37 #msc:46M99 #msc:57M15

paper · pdf · doi:10.48550/arxiv.0903.0144

arxiv created 2009/03/01 · openalex publication_date 2009/03/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give generators and relations for the planar algebras corresponding to ADE subfactors. We also give a basis and an algorithm to express an arbitrary diagram as a linear combination of these basis diagrams.

Cited by

• A planar algebra construction of the Haagerup subfactor

Related

• Skein Theory for Affine A Subfactor Planar Algebras
• Universal skein theory for finite depth subfactor planar algebras
• Stated skein algebras and their representations
• Universal skein theory for group actions
• From subfactor planar algebras to subfactors