A note on generators for finite depth subfactor planar algebras

TL;DR

This paper proves that finite depth subfactor planar algebras can be generated by a single element within a specific box size, simplifying their understanding and analysis.

Contribution

It establishes that subfactor planar algebras of finite depth are generated by one element of bounded size, advancing the structural theory of these algebras.

Findings

Finite depth subfactor planar algebras are generated by a single s-box.

The generating s-box size is bounded by min{k+4, 2k}.

Simplifies the analysis of subfactor planar algebras.

Abstract

We show that a subfactor planar algebra of finite depth $k$ is generated by a single $s$-box, for $s \leq min\{k+4,2k\}$.