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Tetrahedron maps and symmetries of three dimensional integrable discrete equations

2019; American Institute of Physics; Volume: 60; Issue: 12 Linguagem: Inglês

10.1063/1.5124874

1527-2427

Pavlos Kassotakis, Maciej Nieszporski, V. Papageorgiou, Anastasios Tongas,

Advanced Topics in Algebra

A relationship between the tetrahedron equation for maps and the consistency property of integrable discrete equations on $\mathbb{Z}^3$ is investigated. Our approach is a generalization of a method developed in the context of Yang-Baxter maps, based on the invariants of symmetry groups of the lattice equations. The method is demonstrated by a case-by-case analysis of the octahedron type lattice equations classified recently, leading to some new examples of tetrahedron maps and integrable coupled lattice equations.