Central nilpotency of skew braces

TL;DR

This paper develops and compares different notions of central nilpotency in skew braces, algebraic structures linked to quantum Yang-Baxter solutions, enhancing understanding of their algebraic properties.

Contribution

It introduces a theory of central nilpotency for skew braces and compares universal algebraic and $*$-nilpotency notions, advancing the algebraic framework of skew braces.

Findings

Established a central nilpotency theory for skew braces.

Compared universal algebraic and $*$-nilpotency notions.

Clarified algebraic properties related to quantum Yang-Baxter solutions.

Abstract

Skew braces are algebraic structures related to the solutions of the set-theoretic quantum Yang-Baxter equation. We develop the central nilpotency theory for such algebraic structures in the sense of Freese-McKenzie \cite{comm} and we compare the universal algebraic notion of central nilpotency with the notion of right and left $*$-nilpotency developed in \cite{NilpotentType}.