Search results for "yang-baxter equation"
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Left Braces and the Yang-Baxter Equation
2021
L’equació quàntica de Yang-Baxter (YBE per les seues inicials en anglès) és una equació important en la física matemàtica introduïda per Yang en 1967. Un dels seus principals problemes oberts és trobar-ne totes les solucions. En 1992, Drinfeld va definir un subtipus de solucions, les conjuntistes, i va proposar el problema de trobar-les totes. Recentment, una subclasse de les solucions conjuntistes ha sigut molt estudiada: les involutives i no degenerades (a partir d’ara, les anomenarem simplement solucions). En 2007, Rump va introduir una nova estructura algebraica, les brides a esquerra, per a estudiar aquestes solucions, i va demostrar que cada brida a esquerra té una solució de la YBE a…
Left braces and the quantum Yang-Baxter equation
2019
[EN] 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.
On finite involutive Yang–Baxter groups
2021
[EN] A group G is said to be an involutive Yang¿Baxter group, or simply an IYB-group, if it is isomorphic to the permutation group of an involutive, nondegenerate set-theoretic solution of the Yang-Baxter equation. We give new sufficient conditions for a group that can be factorised as a product of two IYB-groups to be an IYB-group. Some earlier results are direct consequences of our main theorem.