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.