A Construction of the "2221" Planar Algebra

Abstract

In this paper, we construct the "2221" subfactor planar algebra by finding it as a subalgebra of the graph planar algebra of its principal graph. In particular, we give a presentation of the "2221" subfactor planar algebra consisting of generators and relations. As a corollary, we have a planar algebra proof of the existence of a subfactor with principal graph "2221". To show the subfactor property, we use the jellyfish algorithm for evaluating closed diagrams. Lastly, we show uniqueness up to conjugation of "2221".

References in corpus (2)

• Skein theory for the D_{2n} planar algebras
• Cyclotomic integers, fusion categories, and subfactors

Cited by in corpus (2)

• The classification of subfactors of index at most 5
• Calculating two-strand jellyfish relations