Braid groups may be defined for every Coxeter diagram. Artin's braid group is of type A. Analogs of Temperley-Lieb, Hecke and Birman-Wenzl algebras exist for B-type. Our general hypothethis is that the braid group of B-type replaces Artin's braid group in most physical applications if the model is equipped with a nontrivial boundary. Solutions of a Potts model with a boundary and the reflection equation illustrate this principle. Braided tensor categories of B-type and dually Coxeter-B braided...

Source: http://arxiv.org/abs/q-alg/9611016v1