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Hopf braces and Yang-Baxter operators


Authors: Iván Angiono, César Galindo and Leandro Vendramin
Journal: Proc. Amer. Math. Soc. 145 (2017), 1981-1995
MSC (2010): Primary 16T05, 16T25
DOI: https://doi.org/10.1090/proc/13395
Published electronically: November 3, 2016
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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.


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Iván Angiono
Affiliation: FaMAF-CIEM (CONICET), Universidad Nacional de Córdoba, Medina Allende s/n, Ciudad Universitaria, 5000 Córdoba, Argentina
Email: angiono@famaf.unc.edu.ar

César Galindo
Affiliation: Departamento de matemáticas, Universidad de los Andes, Carrera 1 N. 18A - 10, Bogotá, Colombia
Email: cn.galindo1116@uniandes.edu.co

Leandro Vendramin
Affiliation: Departamento de Matemática – FCEN, Universidad de Buenos Aires, Pab. I – Ciudad Universitaria (1428) Buenos Aires, Argentina
Email: lvendramin@dm.uba.ar

DOI: https://doi.org/10.1090/proc/13395
Received by editor(s): April 21, 2016
Received by editor(s) in revised form: July 10, 2016
Published electronically: November 3, 2016
Communicated by: Kailash C. Misra
Article copyright: © Copyright 2016 American Mathematical Society