A matrix solution to pentagon equation with anticommuting variables

TL;DR

This paper presents a novel matrix-based solution to the pentagon equation using anticommuting variables on tetrahedral faces, introducing a more quantum-like topological field theory with noncommutative matrix multiplication.

Contribution

It introduces a new matrix solution to the pentagon equation incorporating anticommuting variables, advancing quantum topological field theories.

Findings

Solution uses matrix coordinates on tetrahedron vertices

Incorporates noncommutative matrix multiplication for quantum effects

Enhances the mathematical framework of topological field theories

Abstract

We construct a solution to pentagon equation with anticommuting variables living on two-dimensional faces of tetrahedra. In this solution, matrix coordinates are ascribed to tetrahedron vertices. As matrix multiplication is noncommutative, this provides a "more quantum" topological field theory than in our previous works.