Hopf braces and Yang-Baxter operators

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.

15 pages. Final version. Accepted for publication in Proc. Amer. Math. Soc

References in corpus (3)

• Skew braces and the Yang-Baxter equation
• Bijective 1-cocycles and classification of 3-dimensional Left-symmetric Algebras
• On Engel groups, nilpotent groups, rings, braces and the Yang-Baxter equation

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• Cocommutative q-cycle coalgebra structures on the dual of the truncated polynomial algebra
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