Tetrahedral Zamolodchikov algebras corresponding to Baxter'sL-operators

Tetrahedral Zamolodchikov algebras are structures that occupy an intermediate place between the solutions of the Yang-Baxter equation and its generalization onto 3-dimensional mathematical physics — the tetrahedron equation. These algebras produce solutions to the tetrahedron equation and, besides specific two-layer solutions to the Yang-Baxter equation. Here the tetrahedral Zamolodchikov algebras are studied that arise fromL-operators of the free-fermion case of Baxter's eight-vertex model.