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On the solutions of the local Zamolodchikov tetrahedron equation
Published 25 Mar 2024 in nlin.SI, math-ph, and math.MP | (2403.17070v1)
Abstract: We study the solutions of the local Zamolodhcikov tetrahedron equation in the form of correspondences derived by $3\times 3$ matrices. We present all the associated generators of 4-simplex maps satisfying the local tetrahedron equation. Moreover, we demonstrate that, from some of our solutions, we can recover the 4-simplex extensions of Kashaev--Korepanov--Sergeev and Hirota type tetrahedron maps. Finally, we construct several novel 4-simplex maps.
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