Algebraic structures behind the Yang-Baxterization process

We discuss the process of Yang-Baxterization in representations of the braid group. We discuss the role played by n-CB algebras in Yang-Baxterization. We present diagrams depicting the defining relations for the 4-CB algebras. These relations are illustrated using the isomorphism between the general free algebra generated by {1}, {E-i}, and {G(i)} (the generators of the Birman-Murakami-Wenzl algebra) and Kauffman's tangle algebra.