dorsal/arxiv
View SchemaA note on the eight tetrahedron equations
| Authors | Jarmo Hietarinta, Frank Nijhoff |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9706001 |
| URL | https://arxiv.org/abs/q-alg/9706001 |
| DOI | 10.1063/1.532055 |
Abstract
In this paper we derive from arguments of string scattering a set of eight tetrahedron equations, with different index orderings. It is argued that this system of equations is the proper system that represents integrable structures in three dimensions generalising the Yang-Baxter equation. Under additional restrictions this system reduces to the usual tetrahedron equation in the vertex form. Most known solutions fall under this class, but it is by no means necessary. Comparison is made with the work on braided monoidal 2-categories also leading to eight tetrahedron equations.
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"abstract": "In this paper we derive from arguments of string scattering a set of eight\ntetrahedron equations, with different index orderings. It is argued that this\nsystem of equations is the proper system that represents integrable structures\nin three dimensions generalising the Yang-Baxter equation. Under additional\nrestrictions this system reduces to the usual tetrahedron equation in the\nvertex form. Most known solutions fall under this class, but it is by no means\nnecessary. Comparison is made with the work on braided monoidal 2-categories\nalso leading to eight tetrahedron equations.",
"arxiv_id": "q-alg/9706001",
"authors": [
"Jarmo Hietarinta",
"Frank Nijhoff"
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"math.QA"
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"doi": "10.1063/1.532055",
"title": "A note on the eight tetrahedron equations",
"url": "https://arxiv.org/abs/q-alg/9706001"
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