Ideals in the Temperley Lieb Category

Abstract

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.

Appendix to M. Freedman, A magnetic model with a possible Chern-Simons phase, quant-ph/0110060

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