"Pentagonal Algebra" and Four-Simplex Equation

TL;DR

This paper introduces 'pentagonal algebra,' a novel concept that provides non-trivial solutions to the quantum four-simplex equation, along with examples of its realization and corresponding R-matrices.

Contribution

The paper presents the concept of pentagonal algebra and demonstrates its application in constructing solutions to the quantum four-simplex equation.

Findings

Examples of pentagonal algebra realizations provided

Explicit R-matrices for the quantum four-simplex equation constructed

Non-trivial solutions to the four-simplex equation achieved

Abstract

Some idea, which leads to a non-trivial solution of the quantum four-simplex equation, is exposed in this paper. We call this idea "pentagonal algebra". Few examples of the realisation of this idea are given here, and thus few examples of $R$-matrix for the quantum four-simplex equation are presented.