Constructing skew bracoids via abelian maps, and solutions to the {Y}ang-{B}axter equation

TL;DR

This paper introduces a method to construct skew bracoids using abelian maps, which in turn produce solutions to the Yang-Baxter equation, expanding the toolkit for algebraic solutions in mathematical physics.

Contribution

The paper presents a novel construction of skew bracoids via abelian maps and demonstrates their application in generating solutions to the Yang-Baxter equation.

Findings

Constructed families of skew bracoids using abelian maps.

Generated right non-degenerate solutions to the Yang-Baxter equation.

Provided conditions under which these bracoids yield solutions.

Abstract

We show how one can use the skew braces constructed using abelian maps to generate families of skew bracoids as defined by Martin-Lyons and Truman. Under certain circumstances, these bracoids give right non-degenerate solutions to the Yang-Baxter equation.