Left Braces and the Quantum Yang–Baxter Equation

descriptionPublicationkeyboard_double_arrow_right Article , Other literature type 03 Dec 2018 English Publisher:Cambridge University Press (CUP)Journal:Proceedings of the Edinburgh Mathematical Society, volume 62, pages 595-608 (issn: 0013-0915, eissn: 1464-3839,

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Authors: Meng, Hangyang; Ballester-Bolinches, Adolfo; Esteban Romero, Ramón;

doi: 10.1017/s0013091518000664

handle: 10550/85850

Left Braces and the Quantum Yang–Baxter Equation

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Abstract

AbstractBraces 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.

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University of Valencia
Spain

Keywords

Braces, Yang-Baxter equations, Solvable groups, supersolvable groups, \(p\)-nilpotent group, P-nilpotent group, Yang-Baxter equation, MATEMATICA APLICADA, Yang-Baxter equations and Rota-Baxter operators, Matemàtica, braces

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