Skew left braces of nilpotent type
Ferran Cedo, Agata Smoktunowicz, Leandro Vendramin
TL;DR
This paper investigates the structure of skew left braces of nilpotent type, introducing series of ideals analogous to group central series, and explores their applications to solutions of the Yang-Baxter equation.
Contribution
It defines left and right nilpotent skew left braces using series of ideals and applies these concepts to analyze indecomposable solutions of the Yang-Baxter equation.
Findings
Established analogs of upper central series for skew left braces.
Proved several properties of nilpotent skew left braces.
Applied the structure to classify solutions of the Yang-Baxter equation.
Abstract
We study series of left ideals of skew left braces that are analogs of upper central series of groups. These concepts allow us to define left and right nilpotent skew left braces. Several results related to these concepts are proved and applications to infinite left braces are given. Indecomposable solutions of the Yang-Baxter equation are explored using the structure of skew left braces.
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