A Cyclic Approach to the Annular Temperley-Lieb Category

Details A Cyclic Approach to the Annular Temperley-Lieb Category A Cyclic Approach to the Annular Temperley-Lieb Category

2009-12-07

arxiv.org/abs/0912.1320v1

Mathematics

Quantum Algebra

35 pages, 21 figures

Scientific paper

In 2000, Jones found two copies of the cyclic category in the annular Temperley-Lieb category ATL. We give an abstract presentation of ATL to discuss how these two copies of the cyclic category generate ATL together with the coupling constants and the coupling relations. We then discuss modules over the annular category and homologies of such modules, the latter of which arises from the cyclic viewpoint.

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