From the definition of R above, it follows that for every solution of the Yang–Baxter equation in the tensor product of two n -dimensional vector spaces, there is a corresponding 2-dimensional solvable vertex model where each of the bonds can be in the possible states { 1 , … … , n } , where R is an endomorphism in the space spanned by { | a ⟩ ⟩ ⊗ ⊗ | b ⟩ ⟩ } , 1 ≤ ≤ a , b ≤ ≤ n . This motivates the classification of all the finite-dimensional irreducible representations of a given Quantum algebra in order to find solvable models corresponding to it.