We study three properties of the ℤn⊗ℤn-symmetric lattice model; i.e. the initial condition, the unitarity and the crossing symmetry. The scalar factors appearing in the unitarity and the crossing symmetry are explicitly obtained. The [Formula: see text]-Sklyanin algebra is introduced in the natural framework of the inverse problem for this model. We build both finite- and infinite-dimensional representations of the [Formula: see text]-Sklyanin algebra, and construct an [Formula: see text] generalization of the broken ℤN model. Furthermore, the Yang-Baxter equation for this new model is proved.