Left Braces: Solutions of the Yang-Baxter Equation

Abstract

This is a survey on the theory of left braces, an algebraic structure introduced by Rump as a generalization of Jacobson radical rings to study non-degenerate involutive set-theoretic solutions of the Yang-Baxter equation.

Keywords

• left brace
• Yang-Baxter equation
• set-theoretic solution
• Jacobson radical
• holomorph
• regular subgroup
• monoid of I-type
• group of I-type
• bijetive 1-cocycle
• Garside monoid
• Garside group