A Labelling Scheme for Higher Dimensional Simplex Equations

TL;DR

This paper introduces a labeling scheme that systematically generates higher-dimensional generalizations of the Quantum Yang-Baxter Equation, successfully producing well-known three-simplex equations like ZTE and FME.

Contribution

The paper presents a novel labeling scheme that simplifies the derivation of higher-dimensional simplex equations, including key three-simplex equations.

Findings

Generated the Zamolodchikov tetrahedron equation

Derived the Frenkel and Moore equation

Provided a unified method for higher-dimensional simplex equations

Abstract

We present a succinct way of obtaining all possible higher dimensional generalization of Quantum Yang-Baxter Equation (QYBE). Using the scheme, we could generate the two popular three-simplex equations, namely: Zamolodchikov's tetrahedron equation (ZTE) and Frenkel and Moore equation (FME).