Ideals in the Temperley Lieb Category

Details Ideals in the Temperley Lieb Category Ideals in the Temperley Lieb Category

2002-06-27

arxiv.org/abs/math/0206301v1

Mathematics

Quantum Algebra

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

Scientific paper

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.

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