On multidimensional consistent systems of asymmetric quad-equations

TL;DR

This paper advances the understanding of multidimensional consistency in discrete integrable systems by classifying higher-dimensional systems, including asymmetric and 4D consistent quad-equations, with implications for Bianchi permutability.

Contribution

It provides a classification of higher-dimensional consistent systems of asymmetric quad-equations, extending previous 3D classifications to 4D and beyond.

Findings

Classification of certain 4D consistent systems

Extension of 3D consistent systems to higher dimensions

Proofs of Bianchi permutability applications

Abstract

Multidimensional Consistency becomes more and more important in the theory of discrete integrable systems. Recently, we gave a classification of all 3D consistent 6-tuples of equations with the tetrahedron property, where several novel asymmetric systems have been found. In the present paper we discuss higher-dimensional consistency for 3D consistent systems coming up with this classification. In addition, we will give a classification of certain 4D consistent systems of quad-equations. The results of this paper allow for a proof of the Bianchi permutability among other applications.