Algebraic Structures Behind the Yang-Baxterization Process

We review the Yang-Baxterization process of braid group representations. We discuss the corresponding $n$-CB algebras in the Yang-Baxterization process. We present diagrams of the relations for the $4$-CB algebras. These relations are illustrated using the isomorphism between the general free algebra generated by $\{1\}$, $\{E_i\}$, and $\{G_i\}$ and Kauffman’s tangle algebra.