Abstract
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.
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