Ideals in the Temperley Lieb Category
  We prove the following result: For a generic value of the parameter, the Temperley-Lieb category has no non-zero, proper tensor ideal. When the parameter $d$ is equal to $2\cos(\pi/n)$ for some $n \ge 3$, then the Temperley-Lieb category has exactly one non-zero, proper ideal, namely the ideal of negligible morphisms. 
Frederick M. Goodman, Hans Wenzl