Skew Braces from a model-theoretic point of view 1

TL;DR

This paper explores the model-theoretic properties of skew braces, focusing on their solubility and nilpotency, to better understand their algebraic structure in relation to the Yang-Baxter equation.

Contribution

It introduces a model-theoretic perspective on skew braces, analyzing their solubility and nilpotency, which are new approaches in the study of these algebraic structures.

Findings

Skew braces can be characterized as model-theoretically tame structures.

Solubility and nilpotency are examined within the framework of model theory.

The paper provides new insights into the algebraic and model-theoretic properties of skew braces.

Abstract

Skew braces are one of the main algebraic tools controlling the structure of a non-degenerate bijective set-theoretic solution of the Yang-Baxter equation. The aim of this paper is to study model-theoretically tame skew braces, with particular attention to the notions of solubility and nilpotency.