A cuprate superconductor model based on the analogy with atomic nuclei was presented to have an su(3) algebraic structure by Iachello. Our previous work showed that the mean-field approximation Hamiltonian can be expressed as a linear function of the generator of su(3) algebra. Through the realization of the algebra generator, an sus(1,1) ⊕ sud(1,1) algebraic structure is shown. By using the unitary transformation of the coherent operator U(θ,φ), the gap equations and the eigenvalues of the reduced Hamiltonian are obtained. The analysis of the physical model through different algebraic structures leads to different particular results.