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Left braces and the quantum Yang-Baxter equation

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Left braces and the quantum Yang-Baxter equation

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dc.contributor.author Meng, H. es_ES
dc.contributor.author BALLESTER BOLINCHES, ADOLFO es_ES
dc.contributor.author Esteban Romero, Ramón es_ES
dc.date.accessioned 2020-11-07T04:32:21Z
dc.date.available 2020-11-07T04:32:21Z
dc.date.issued 2019-05 es_ES
dc.identifier.issn 0013-0915 es_ES
dc.identifier.uri http://hdl.handle.net/10251/154382
dc.description.abstract [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. es_ES
dc.description.sponsorship This work was supported by the research grant MTM2014-54707-C3-1-P from the Ministerio de Economia y Competitividad, Spanish Government, and FEDER, European Union, and PROMETEO/2017/057 from Generalitat (Valencian Community, Spain). The first author was supported by grant number 201606890006 of the China Scholarship Council. es_ES
dc.language Inglés es_ES
dc.publisher Cambridge University Press es_ES
dc.relation.ispartof Proceedings of the Edinburgh Mathematical Society es_ES
dc.rights Reserva de todos los derechos es_ES
dc.subject P-nilpotent group es_ES
dc.subject Braces es_ES
dc.subject Yang-Baxter equation es_ES
dc.subject.classification MATEMATICA APLICADA es_ES
dc.title Left braces and the quantum Yang-Baxter equation es_ES
dc.type Artículo es_ES
dc.identifier.doi 10.1017/S0013091518000664 es_ES
dc.relation.projectID info:eu-repo/grantAgreement/MINECO//MTM2014-54707-C3-1-P/ES/PROPIEDADES ARITMETICAS Y ESTRUCTURALES DE GRUPOS Y SEMIGRUPOS I/ es_ES
dc.relation.projectID info:eu-repo/grantAgreement/GVA//PROMETEO%2F2017%2F057/ es_ES
dc.relation.projectID info:eu-repo/grantAgreement/CSC//201606890006/ es_ES
dc.rights.accessRights Abierto es_ES
dc.contributor.affiliation Universitat Politècnica de València. Departamento de Matemática Aplicada - Departament de Matemàtica Aplicada es_ES
dc.description.bibliographicCitation Meng, H.; Ballester Bolinches, A.; Esteban Romero, R. (2019). Left braces and the quantum Yang-Baxter equation. Proceedings of the Edinburgh Mathematical Society. 62(2):595-608. https://doi.org/10.1017/S0013091518000664 es_ES
dc.description.accrualMethod S es_ES
dc.relation.publisherversion https://doi.org/10.1017/S0013091518000664 es_ES
dc.description.upvformatpinicio 595 es_ES
dc.description.upvformatpfin 608 es_ES
dc.type.version info:eu-repo/semantics/publishedVersion es_ES
dc.description.volume 62 es_ES
dc.description.issue 2 es_ES
dc.relation.pasarela S\386700 es_ES
dc.contributor.funder Generalitat Valenciana es_ES
dc.contributor.funder China Scholarship Council es_ES
dc.contributor.funder European Regional Development Fund es_ES
dc.contributor.funder Ministerio de Economía y Competitividad es_ES
dc.description.references Yang, C. N. (1967). Some Exact Results for the Many-Body Problem in one Dimension with Repulsive Delta-Function Interaction. Physical Review Letters, 19(23), 1312-1315. doi:10.1103/physrevlett.19.1312 es_ES
dc.description.references Smoktunowicz, A. (2018). On Engel groups, nilpotent groups, rings, braces and the Yang-Baxter equation. Transactions of the American Mathematical Society, 370(9), 6535-6564. doi:10.1090/tran/7179 es_ES
dc.description.references Etingof, P., Schedler, T., & Soloviev, A. (1999). Set-theoretical solutions to the quantum Yang-Baxter equation. Duke Mathematical Journal, 100(2), 169-209. doi:10.1215/s0012-7094-99-10007-x es_ES
dc.description.references Cedó, F., Jespers, E., & Okniński, J. (2014). Braces and the Yang–Baxter Equation. Communications in Mathematical Physics, 327(1), 101-116. doi:10.1007/s00220-014-1935-y es_ES
dc.description.references Cedó, F., Gateva-Ivanova, T., & Smoktunowicz, A. (2017). On the Yang–Baxter equation and left nilpotent left braces. Journal of Pure and Applied Algebra, 221(4), 751-756. doi:10.1016/j.jpaa.2016.07.014 es_ES
dc.description.references Bachiller, D., Cedó, F., & Jespers, E. (2016). Solutions of the Yang–Baxter equation associated with a left brace. Journal of Algebra, 463, 80-102. doi:10.1016/j.jalgebra.2016.05.024 es_ES
dc.description.references Rump, W. (2007). Braces, radical rings, and the quantum Yang–Baxter equation. Journal of Algebra, 307(1), 153-170. doi:10.1016/j.jalgebra.2006.03.040 es_ES
dc.description.references Smoktunowicz, A. (2018). A note on set-theoretic solutions of the Yang–Baxter equation. Journal of Algebra, 500, 3-18. doi:10.1016/j.jalgebra.2016.04.015 es_ES
dc.description.references Kurzweil, H., & Stellmacher, B. (2004). The Theory of Finite Groups. Universitext. doi:10.1007/b97433 es_ES


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