Yang-Baxter Equation on Two-Dimensional Lattice and Some Infinite Dimensional Algebras

We show that the Yang-Baxter equation is equivalent to the associativity of the algebra generated by non-commuting link operators. Starting from these link operators we build out the (FFZ) algebras, the $s{\mathrm{\ell }}_q(2)$ is derived by considering a special combination of the generators of (FFZ) algebra.