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.