Temperley–Lieb algebra

Summary

The Temperley–Lieb algebra $TL_n(\delta)$ is an algebra with generators $e_1, \dots, e_{n-1}$ and simple relations depending on a parameter $\delta$. It first appeared in the work of Temperley and Lieb on lattice models of statistical mechanics. Jones found it again in the study of subfactors, and it underlies the Jones polynomial of knots. It has a basis of planar diagrams, and its dimension is the Catalan number $\frac{1}{n+1}\binom{2n}{n}$.