# On a presentation of the spin planar algebra

## TL;DR

This paper introduces an abstract planar algebra through generators and relations, analyzes its structure, and identifies it with Jones' spin planar algebra, contributing to the understanding of algebraic structures in quantum topology.

## Contribution

It provides a new presentation of Jones' spin planar algebra using generators and relations, enhancing the algebra's structural understanding.

## Key findings

- Established an abstract planar algebra with generators and relations.
- Identified the algebra with Jones' spin planar algebra.
- Analyzed structural properties of the algebra.

## Abstract

We define a certain abstract planar algebra by generators and relations, study various aspects of its structure, and then identify it with Jones' spin planar algebra.