Hopf braces and Yang-Baxter operators

TL;DR

This paper introduces Hopf braces, a novel algebraic structure that generalizes classical braces and connects to the Yang-Baxter equation, offering a new framework for studying algebraic solutions in mathematical physics.

Contribution

It defines Hopf braces, extending classical braces to a non-commutative setting, and links them to Lie-theoretic structures like left symmetric algebras.

Findings

Hopf braces encompass Rump's braces and their non-commutative variants.

Classical brace properties remain valid within Hopf braces.

Provides a new algebraic framework for Yang-Baxter solutions.

Abstract

This paper introduces Hopf braces, a new algebraic structure related to the Yang-Baxter equation which include Rump's braces and their non-commutative generalizations as particular cases. Several results of classical braces are still valid in our context. Furthermore, Hopf braces provide the right setting for considering left symmetric algebras as Lie-theoretical analogs of braces.