On Quadrirational Yang-Baxter Maps

TL;DR

This paper classifies quadrirational Yang-Baxter maps, linking their properties to singularity invariance and geometric symmetries, and introduces new families of such maps.

Contribution

It provides a characterization of quadrirational Yang-Baxter maps via singularity invariance and geometric symmetries, expanding the known families of these maps.

Findings

Maps satisfy the Yang-Baxter relation under certain conditions.

New families of Yang-Baxter maps are identified.

Maps are characterized by singularity invariance and geometric symmetries.

Abstract

We use the classification of the quadrirational maps given by Adler, Bobenko and Suris to describe when such maps satisfy the Yang-Baxter relation. We show that the corresponding maps can be characterized by certain singularity invariance condition. This leads to some new families of Yang-Baxter maps corresponding to the geometric symmetries of pencils of quadrics.