A note on the eight tetrahedron equations

Details A note on the eight tetrahedron equations A note on the eight tetrahedron equations

1997-06-02

arxiv.org/abs/q-alg/9706001v1

Mathematics

Quantum Algebra

18 pages in LaTeX, to appear in J. Math. Phys

Scientific paper

10.1063/1.532055

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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