Archivo de la etiqueta: Yang-Baxter equation

Paper «The Structure Group and the Permutation Group of a Set-Theoretic Solution of the Quantum Yang–Baxter Equation» published in Mediterr. J. Math.

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A. Ballester-Bolinches, R. Esteban-Romero, N. Fuster-Corral, H. Meng.
The Structure Group and the Permutation Group of a Set-Theoretic Solution of the Quantum Yang–Baxter Equation.
Mediterr. J. Math, 18: Article number 145, 2021.

doi: 10.1007/s00009-021-01793-7

Abstract:

We describe the left brace structure of the structure group and the permutation group associated with an involutive, non-degenerate set-theoretic solution of the quantum Yang–Baxter equation using the Cayley graph of its permutation group with respect to its natural generating system. We use our descriptions of the additions in both braces to obtain new properties of the structure and the permutation groups and to recover some known properties of these groups in a more transparent way.

2020 Mathematics Subject Classification: 16T25, 05C25, 20F05, 20F65

Keywords: left brace, Yang-Baxter equation, Cayley graph, structure group.

Paper «On finite involutive Yang-Baxter groups» published in Proc. Amer. Math. Soc.

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H. Meng, A. Ballester-Bolinches, R. Esteban-Romero, and N. Fuster-Corral.
On finite involutive Yang-Baxter groups.
Proc. Amer. Math. Soc., 149(2):793–804, 2021.

doi:10.1090/proc/15283

Abstract

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.

2020 Mathematics Subject Classification: Primary 81R50; Secondary 20F29, 20B35, 20F16, 20C05, 16S34, 16T25

Keywords: Finite left brace, Yang-Baxter equation, involutive nondegenerate solutions, involutive Yang-Baxter group

Seminaris Paola Stefanelli i Marzia Mazzotta 30/10/2019 16.30

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Oct ’19
30
16:30

Benvolgudes companyes, benvolguts companys,

El proper dimecres 30 d’octubre, a partir de les 16.30 hores, al seminari d’Àlgebra de la Facultat de Matemàtiques de la Universitat de València (2n pis) es duran a terme els següents seminaris:

  • 16.30 Paola Stefanelli (Università del Salento, Lecce, Pulla, Itàlia) «Set-theoretical solutions to the Yang-Baxter equation of finite order» (resum)
  • 17.00 Marzia Mazzotta (Università del Salento, Lecce, Pulla, Itàlia) «Recent developments of the pentagon equation with an application to the Yang-Baxter equation» (resum)

Us convidem a assistir-hi.

Paper «Left braces and the quantum Yang-Baxter equation» published in Proc. Edinburgh Math. Soc.

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The following paper has been published:
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El següent article ha sigut publicat:

H. Meng, A. Ballester-Bolinches y R. Esteban-Romero.
Left braces and the quantum Yang-Baxter equation.
Proc. Edinburgh Math. Soc., 62(2):595–608, 2019.

doi:10.1017/S0013091518000664

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.

2010 Mathematics Subject Classification: 26T25, 20F16

Keywords: p-nilpotent group, braces, Yang-Baxter equation