Letters in Mathematical Physics

, Volume 30, Issue 3, pp 189-206

First online:

The blob algebra and the periodic Temperley-Lieb algebra

  • Paul MartinAffiliated withDepartment of Mathematics, City University
  • , Hubert SaleurAffiliated withDepartment of Mathematics and Department of Physics, University of Southern California

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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. 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. We complete the analysis using results from the study of the blob algebra.

Mathematics Subject Classifications (1991)

16D90 81R05 81R10 82B20