Two-state spectral-free solutions of the Frenkel-Moore simplex equation

Whilst many solutions have been found for the quantum Yang-Baxter equation (QYBE), there are fewer known solutions available for its higher dimensional generalizations: Zamolodchikov`s tetrahedron equation (ZTE) and Frenkel and Moore`s simplex equation (FME). In this paper, we present families of solutions to the FME which may help us to understand more about higher dimensional generalization of the QYBE.