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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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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

Por favor, use este identificador para citar o enlazar este ítem: http://hdl.handle.net/10251/154382

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Title: Left braces and the quantum Yang-Baxter equation
Author: Meng, H. BALLESTER BOLINCHES, ADOLFO Esteban Romero, Ramón
UPV Unit: Universitat Politècnica de València. Departamento de Matemática Aplicada - Departament de Matemàtica Aplicada
Issued date:
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 ...[+]
Subjects: P-nilpotent group , Braces , Yang-Baxter equation
Copyrigths: Reserva de todos los derechos
Source:
Proceedings of the Edinburgh Mathematical Society. (issn: 0013-0915 )
DOI: 10.1017/S0013091518000664
Publisher:
Cambridge University Press
Publisher version: https://doi.org/10.1017/S0013091518000664
Project ID:
info:eu-repo/grantAgreement/MINECO//MTM2014-54707-C3-1-P/ES/PROPIEDADES ARITMETICAS Y ESTRUCTURALES DE GRUPOS Y SEMIGRUPOS I/
GV/PROMETEO/2017/057
CSC/201606890006
Thanks:
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, ...[+]
Type: Artículo

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

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

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 [+]
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

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

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

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

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

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

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

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

Kurzweil, H., & Stellmacher, B. (2004). The Theory of Finite Groups. Universitext. doi:10.1007/b97433

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