The structure skew brace associated with a finite non-degenerate solution of the Yang-Baxter equation is finitely presented

TL;DR

This paper proves that the algebraic structure called a skew brace, associated with finite non-degenerate solutions to the Yang-Baxter equation, can be described with a finite set of generators and relations.

Contribution

It establishes that the structure skew brace for such solutions is finitely presented, advancing understanding of their algebraic properties.

Findings

The structure skew brace is finitely presented.

Finite non-degenerate solutions lead to finitely describable algebraic structures.

Provides a foundation for further algebraic analysis of Yang-Baxter solutions.

Abstract

The aim of this paper is to show that the structure skew brace associated with a finite non-degenerate solution of the Yang-Baxter equation is finitely presented.