Temperley-Lieb at roots of unity, a fusion category and the Jones quotient

K. Iohara, G. I. Lehrer, R. B. Zhang

When the parameter $q$ is a root of unity, the Temperley-Lieb algebra $T{L}_n(q)$ is non-semisimple for almost all $n$. In this work, using cellular methods, we give explicit generat…