Temperley-Lieb diagram algebra
= Temperley-Lieb diagram algebra
{c}
{title2=$e_i^2=\delta e_i,\quad e_ie_{i+1}e_i=e_i$}
The Temperley-Lieb diagram algebra is generated by planar cap-cup <tangles>, with composition by stacking and each closed circle replaced by $\delta$. Its local relations $e_i^2=\delta e_i$ and $e_ie_{i+1}e_i=e_i$ make the second and third <Reidemeister moves> direct algebraic identities for $R_i=A I+A^{-1}e_i$ when $\delta=-A^2-A^{-2}$.