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Abstract:

Braces and linear cycle sets are algebraic structures playing a major role in the classification of involutive set-theoretic solutions to the Yang-Baxter equation. This paper introduces two versions of their (co)homology theories. These theories mix the Harrison (co)homology for the abelian group structure and the (co)homology theory for general cycle sets, developed earlier by the authors. Different classes of brace extensions are completely classified in terms of second cohomology groups. © 2016 Mathematical Sciences Publishers.

Registro:

Documento: Artículo
Título:Cohomology and extensions of braces
Autor:Lebed, V.; Vendramin, L.
Filiación:Laboratoire De Mathématiques, Jean Leray Université De Nantes, 2 Rue De La Houssinière BP 92208, Nantes Cedex 3, 44322, France
Departamento De Matemática, Fcen Universidad De Buenos Aires, Pabellón 1, Buenos Aires, 1428, Argentina
Palabras clave:Brace; Cohomology; Cycle set; Extension; Yang-Baxter equation
Año:2016
Volumen:284
Número:1
Página de inicio:191
Página de fin:212
DOI: http://dx.doi.org/10.2140/pjm.2016.284.191
Título revista:Pacific Journal of Mathematics
Título revista abreviado:Pac. J. Math.
ISSN:00308730
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00308730_v284_n1_p191_Lebed

Referencias:

  • Bachiller, D., 'Classification of braces of order p3' (2015) J. Pure Appl. Algebra, 219 (8), pp. 3568-3603. , MR Zbl
  • Bachiller, D., (2015) "Examples of simple left braces", , preprint, arXiv
  • Bachiller, D., Cedo, F., Jespers, E., (2015) 'Solutions of the Yang-Baxter equation associated with a left brace', , preprint, arXiv
  • Bachiller, D., Cedo, F., Jespers, E., Okninski, J., (2015) 'A family of irretractable square-free solutions of the Yang-Baxter equation', , preprint, arXiv
  • Ben David, N., Ginosar, Y., 'On groups of I-type and involutive Yang-Baxter groups' (2016) J. Algebra, 458, pp. 197-206. , MR
  • Catino, F., Rizzo, R., 'Regular subgroups of the affine group and radical circle algebras' (2009) Bull. Aust. Math. Soc, 79 (1), pp. 103-107. , MR Zbl
  • Catino, F., Colazzo, I., Stefanelli, P., 'On regular subgroups of the affine group' (2015) Bull. Aust. Math. Soc, 91 (1), pp. 76-85. , MR Zbl
  • Catino, F., Colazzo, I., Stefanelli, P., 'Regular subgroups of the affine group and asymmetric product of radical braces' (2016) J. Algebra, 455, pp. 164-182. , MR Zbl
  • Cedó, F., Jespers, E., Okniński, J., 'Retractability of set theoretic solutions of the Yang-Baxter equation' (2010) Adv. Math, 224 (6), pp. 2472-2484. , MR Zbl
  • Cedó, F., Jespers, E., del Río, á., 'Involutive Yang-Baxter groups' (2010) Trans. Amer. Math. Soc, 362 (5), pp. 2541-2558. , MR Zbl
  • Cedó, F., Jespers, E., Okniński, J., 'Braces and the Yang-Baxter equation' (2014) Comm. Math. Phys, 327 (1), pp. 101-116. , MR Zbl
  • Chouraqui, F., 'Garside groups and Yang-Baxter equation' (2010) Comm. Algebra, 38 (12), pp. 4441-4460. , MR Zbl
  • Dehornoy, P., 'Set-theoretic solutions of the Yang-Baxter equation, RC-calculus, and Garside germs' (2015) Adv. Math, 282, pp. 93-127. , MR Zbl
  • Etingof, P., Schedler, T., Soloviev, A., 'Set-theoretical solutions to the quantum Yang-Baxter equation' (1999) Duke Math. J, 100 (2), pp. 169-209. , MR Zbl
  • Gateva-Ivanova, T., 'A combinatorial approach to the set-theoretic solutions of the Yang-Baxter equation' (2004) J. Math. Phys, 45 (10), pp. 3828-3858. , MR Zbl
  • Gateva-Ivanova, T., (2015) 'Set-theoretic solutions of the Yang-Baxter equation, Braces, and Symmetric groups', , preprint. arXiv
  • Gateva-Ivanova, T., Cameron, P., 'Multipermutation solutions of the Yang-Baxter equation' (2012) Comm. Math. Phys, 309 (3), pp. 583-621. , MR Zbl
  • Gateva-Ivanova, T., Majid, S., 'Matched pairs approach to set theoretic solutions of the Yang-Baxter equation' (2008) J. Algebra, 319 (4), pp. 1462-1529. , MR Zbl
  • Gateva-Ivanova, T., Van den Bergh, M., 'Semigroups of I-type' (1998) J. Algebra, 206 (1), pp. 97-112. , MR Zbl
  • Jespers, E., Okniński, J., 'Monoids and groups of I-type' (2005) Algebr. Represent. Theory, 8 (5), pp. 709-729. , MR Zbl
  • Lebed, V., Vendramin, L., (2015) 'Homology of left non-degenerate settheoretic solutions to the Yang-Baxter equation', , preprint. arXiv
  • Lu, J.-H., Yan, M., Zhu, Y.-C., 'On the set-theoretical Yang-Baxter equation' (2000) Duke Math. J, 104 (1), pp. 1-18. , MR Zbl
  • Rump, W., 'A decomposition theorem for square-free unitary solutions of the quantum Yang-Baxter equation' (2005) Adv. Math, 193 (1), pp. 40-55. , MR Zbl
  • Rump, W., 'Braces, radical rings, and the quantum Yang-Baxter equation' (2007) J. Algebra, 307 (1), pp. 153-170. , MR Zbl
  • Rump, W., 'Semidirect products in algebraic logic and solutions of the quantum Yang-Baxter equation' (2008) J. Algebra Appl, 7 (4), pp. 471-490. , MR Zbl
  • Rump, W., 'The brace of a classical group' (2014) Note Mat, 34 (1), pp. 115-144. , MR Zbl
  • Smoktunowicz, A., (2015) A note on set-theoretic solutions of the Yang-Baxter equation, , preprint. arXiv
  • Smoktunowicz, A., (2015) On Engel groups, nilpotent groups, rings, braces and the Yang-Baxter equation, , preprint, arXiv
  • Soloviev, A., 'Non-unitary set-theoretical solutions to the quantum Yang-Baxter equation' (2000) Math. Res. Lett, 7 (5-6), pp. 577-596. , MR Zbl
  • 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. 2064-2076. , MR Zbl

Citas:

---------- APA ----------
Lebed, V. & Vendramin, L. (2016) . Cohomology and extensions of braces. Pacific Journal of Mathematics, 284(1), 191-212.
http://dx.doi.org/10.2140/pjm.2016.284.191
---------- CHICAGO ----------
Lebed, V., Vendramin, L. "Cohomology and extensions of braces" . Pacific Journal of Mathematics 284, no. 1 (2016) : 191-212.
http://dx.doi.org/10.2140/pjm.2016.284.191
---------- MLA ----------
Lebed, V., Vendramin, L. "Cohomology and extensions of braces" . Pacific Journal of Mathematics, vol. 284, no. 1, 2016, pp. 191-212.
http://dx.doi.org/10.2140/pjm.2016.284.191
---------- VANCOUVER ----------
Lebed, V., Vendramin, L. Cohomology and extensions of braces. Pac. J. Math. 2016;284(1):191-212.
http://dx.doi.org/10.2140/pjm.2016.284.191