Yang-baxterization of the algebra BHN(l, m)

The algebra BHn(l, m) is defined by two sets of generators satisfying the relations of the Artin braid group algebra and the Hecke algebra of projectors. Furthermore, these generators are combined by additional relations in a way which generalizes the Birman-Wenzl algebra Cn(l, m). In this paper we investigate the Yang-Baxterization of the algebra BHn(l, m), that is, the construction of solutions of the Yang-Baxter equation from realizations of the algebra. A general expression is given which associates to every representation of the algebra two solutions of the Yang-Baxter equation. The expression generalizes the known one for the algebra Cn(l, m). We discuss a particular example.