A Construction of the "2221" Planar Algebra

Understand

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.