Universal skein theory for finite depth subfactor planar algebras

TL;DR

This paper provides an explicit finite presentation for finite depth subfactor planar algebras, demonstrating they are singly generated with finitely many relations, advancing the understanding of their algebraic structure.

Contribution

It introduces a universal skein theory that explicitly characterizes finite depth subfactor planar algebras with a finite set of generators and relations.

Findings

Finite depth subfactor planar algebras have explicit finite presentations.

Such planar algebras are singly generated.

They are governed by finitely many relations.

Abstract

We describe an explicit finite presentation for a finite depth subfactor planar algebra. We also show that such planar algebras are singly generated with the generator subject to finitely many relations.