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Left Braces and the Quantum Yang–Baxter Equation

Part of: Hopf algebras, quantum groups and related topics Special aspects of infinite or finite groups

Published online by Cambridge University Press:  03 December 2018

H. Meng ,
A. Ballester-Bolinches  and
R. Esteban-Romero
H. Meng*
Affiliation:
Departament de Matemàtiques, Universitat de València, 46100 Burjassot, València, Spain (hangyangmenges@gmail.com; Adolfo.Ballester@uv.es; Ramon.Esteban@uv.es)
A. Ballester-Bolinches
Affiliation:
Departament de Matemàtiques, Universitat de València, 46100 Burjassot, València, Spain (hangyangmenges@gmail.com; Adolfo.Ballester@uv.es; Ramon.Esteban@uv.es)
R. Esteban-Romero
Affiliation:
Departament de Matemàtiques, Universitat de València, 46100 Burjassot, València, Spain (hangyangmenges@gmail.com; Adolfo.Ballester@uv.es; Ramon.Esteban@uv.es)
*
*Corresponding author.
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Abstract

Braces were introduced by Rump in 2007 as a useful tool in the study of the set-theoretic solutions of the Yang–Baxter equation. In fact, several aspects of the theory of finite left braces and their applications in the context of the Yang–Baxter equation have been extensively investigated recently. The main aim of this paper is to introduce and study two finite brace theoretical properties associated with nilpotency, and to analyse their impact on the finite solutions of the Yang–Baxter equation.

Keywords

p-nilpotent groupbracesYang–Baxter equation

MSC classification

Primary: 16T25: Yang-Baxter equations
Secondary: 20F16: Solvable groups, supersolvable groups
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 62 , Issue 2 , May 2019 , pp. 595 - 608
Copyright
Copyright © Edinburgh Mathematical Society 2018 

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Footnotes

†

Permanent address: Institut Universitari de Matemàtica Pura i Aplicada, Universitat Politècnica de València, Camí de Vera, s/n, 46022 València, Spain, email: resteban@mat.upv.es.

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