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Abstract:

We prove that a finite non-degenerate involutive set-theoretic solution (X, r) of the Yang{Baxter equation is a multipermutation solution if and only if its structure group G(X, r) admits a left ordering or equivalently it is poly-Z. © 2018 Universitat Autonoma de Barcelona. All rights reserved.

Registro:

Documento: Artículo
Título:A characterization of finite multipermutation solutions of the Yang-Baxter equation
Autor:Bachiller, D.; Cedó, F.; Vendramin, L.
Filiación:Departament de Matemàtiques, Universitat Autònoma de Barcelona, Bellaterra (Barcelona), 08193, Spain
IMAS-CONICET, Departamento de Matemática, FCEN, Universidad de Buenos Aires, Pabellón 1, Ciudad Universitaria, Buenos Aires, C1428EGA, Argentina
Palabras clave:Brace; Ordered groups; Poly-(infinite cyclic) group; Set-theoretic solution; Yang-Baxter equation
Año:2018
Volumen:62
Número:2
Página de inicio:641
Página de fin:649
DOI: http://dx.doi.org/10.5565/PUBLMAT6221809
Título revista:Publicacions Matematiques
Título revista abreviado:Publ. Mat.
ISSN:02141493
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_02141493_v62_n2_p641_Bachiller

Referencias:

  • Bachiller, D., Extensions, matched products, and simple braces (2018) J. Pure Appl. Algebra, 222 (7), pp. 1670-1691
  • Bachiller, D., Cedffo, F., Jespers, E., Okniński, J., A family of irretractable square-free solutions of the Yang-Baxter equation (2017) Forum Math., 29 (6), pp. 1291-1306
  • Cedó, F., Gateva-Ivanova, T., Smoktunowicz, A., On the Yang-Baxter equation and left nilpotent left braces (2017) J. Pure Appl. Algebra, 221 (4), pp. 751-756
  • Cedó, F., Jespers, E., Okniński, J., Retractability of set theoretic solutions of the Yang-Baxter equation (2010) Adv. Math., 224 (6), pp. 2472-2484
  • Cedó, F., Jespers, E., Okniński, J., Braces and the Yang-Baxter equation (2014) Comm. Math. Phys., 327 (1), pp. 101-116
  • Chouraqui, F., Garside groups and Yang-Baxter equation (2010) Comm. Algebra, 38 (12), pp. 4441-4460
  • Chouraqui, F., Left orders in Garside groups (2016) Internat. J. Algebra Comput., 26 (7), pp. 1349-1359
  • Dehornoy, P., Set-theoretic solutions of the Yang-Baxter equa-tion, RC-calculus, and Garside germs (2015) Adv. Math., 282, pp. 93-127
  • Drinfeld, V.G., On some unsolved problems in quantum group theory (1992) Quantum Groups, pp. 1-8. , (Leningrad, 1990), Lecture Notes in Math. 1510, Springer, Berlin
  • Etingof, P., Schedler, T., Soloviev, A., Set-theoretical solutions to the quantum Yang-Baxter equation (1999) Duke Math. J., 100 (2), pp. 169-209
  • Farkas, D.R., Crystallographic groups and their mathematics (1981) Rocky Mountain J. Math., 11 (4), pp. 511-551
  • Gateva-Ivanova, T., A combinatorial approach to the set-theo-retic solutions of the Yang-Baxter equation (2004) J. Math. Phys., 45 (10), pp. 3828-3858
  • Gateva-Ivanova, T., (2015) Set-theoretic Solutions of the Yang-Baxter Equation, Braces, and Symmetric Groups, , Preprint
  • Gateva-Ivanova, T., Cameron, P., Multipermutation solu-tions of the Yang-Baxter equation (2012) Comm. Math. Phys., 309 (3), pp. 583-621
  • Gateva-Ivanova, T., Van den Bergh, M., Semigroups of i-type (1998) J. Algebra, 206 (1), pp. 97-112
  • Guarnieri, L., Vendramin, L., Skew braces and the Yang-Baxter equation (2017) Math. Comp., 86 (307), pp. 2519-2534
  • Jespers, E., Okniński, J., Monoids and groups of I-type (2005) Al-gebr. Represent. Theory, 8 (5), pp. 709-729
  • Rotman, J.J., (1995) An Introduction to the Theory of Groups, , Fourth edition, Graduate Texts in Mathematics 148, Springer-Verlag, New York
  • Rump, W., Braces, radical rings, and the quantum Yang-Baxter equation (2007) J. Algebra, 307 (1), pp. 153-170
  • Vendramin, L., Extensions of set-theoretic solutions of the Yang-Baxter equation and a conjecture of Gateva-Ivanova (2016) J. Pure Appl. Algebra, 220 (5), pp. 206-2076

Citas:

---------- APA ----------
Bachiller, D., Cedó, F. & Vendramin, L. (2018) . A characterization of finite multipermutation solutions of the Yang-Baxter equation. Publicacions Matematiques, 62(2), 641-649.
http://dx.doi.org/10.5565/PUBLMAT6221809
---------- CHICAGO ----------
Bachiller, D., Cedó, F., Vendramin, L. "A characterization of finite multipermutation solutions of the Yang-Baxter equation" . Publicacions Matematiques 62, no. 2 (2018) : 641-649.
http://dx.doi.org/10.5565/PUBLMAT6221809
---------- MLA ----------
Bachiller, D., Cedó, F., Vendramin, L. "A characterization of finite multipermutation solutions of the Yang-Baxter equation" . Publicacions Matematiques, vol. 62, no. 2, 2018, pp. 641-649.
http://dx.doi.org/10.5565/PUBLMAT6221809
---------- VANCOUVER ----------
Bachiller, D., Cedó, F., Vendramin, L. A characterization of finite multipermutation solutions of the Yang-Baxter equation. Publ. Mat. 2018;62(2):641-649.
http://dx.doi.org/10.5565/PUBLMAT6221809