Problems on Skew Left Braces

Abstract

Braces were introduced by Rump as a generalization of Jacobson radical rings. It turns out that braces allow us to use ring-theoretic and group-theoretic methods for studying involutive solutions to the Yang–Baxter equation. If braces are replaced by skew braces, then one can use similar methods for studying not necessarily involutive solutions. Here we collect problems related to (skew) braces and set-theoretic solutions to the Yang-Baxter equation.

Keywords

• brace
• skew brace
• Yang-Baxter equation
• radical ring
• nil ring
• regular subgroup
• circle algebra