The Blob Algebra and the Periodic Temperley-Lieb Algebra

Details The Blob Algebra and the Periodic Temperley-Lieb Algebra The Blob Algebra and the Periodic Temperley-Lieb Algebra

1993-02-19

arxiv.org/abs/hep-th/9302094v1

Physics

High Energy Physics

High Energy Physics - Theory

12 pages

Scientific paper

10.1007/BF00805852

We determine the structure of two variations on the Temperley-Lieb algebra, both used for dealing with special kinds of boundary conditions in statistical mechanics models. The first is a new algebra, the `blob' algebra (the reason for the name will become obvious shortly!). We determine both the generic and all the exceptional structures for this two parameter algebra. The second is the periodic Temperley-Lieb algebra. The generic structure and part of the exceptional structure of this algebra have already been studied. Here we complete the analysis, using results from the study of the blob algebra.

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