Abstract:
This paper introduces Hopf braces, a new algebraic structure related to the Yang–Baxter equation, which include Rump’s braces and their non-commutative generalizations as particular cases. Several results of classical braces are still valid in our context. Furthermore, Hopf braces provide the right setting for considering left symmetric algebras as Lie-theoretical analogs of braces. © 2016 American Mathematical Society.
Registro:
Documento: |
Artículo
|
Título: | Hopf braces and Yang-Baxter operators |
Autor: | Angiono, I.; Galindo, C.; Vendramin, L. |
Filiación: | FaMAF-CIEM (CONICET), Universidad Nacional de Córdoba, Medina Allende s/n, Ciudad Universitaria, Córdoba, 5000, Argentina Departamento de matemáticas, Universidad de los Andes, Carrera 1 N. 18A - 10, Bogotá, Colombia Departamento de Matemática – FCEN, Universidad de Buenos Aires, Pab. I – Ciudad Universitaria (1428), Buenos Aires, Argentina
|
Año: | 2017
|
Volumen: | 145
|
Número: | 5
|
Página de inicio: | 1981
|
Página de fin: | 1995
|
DOI: |
http://dx.doi.org/10.1090/proc/13395 |
Título revista: | Proceedings of the American Mathematical Society
|
Título revista abreviado: | Proc. Am. Math. Soc.
|
ISSN: | 00029939
|
Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00029939_v145_n5_p1981_Angiono |
Referencias:
- Abe, E., (1980) Hopf Algebras, Volume 74 of Cambridge Tracts in Mathematics, , Cambridge University Press, Cambridge, Translated from the Japanese by Hisae Kinoshita and Hiroko Tanaka
- Bachiller, D., Classification of braces of order p3 (2015) J. Pure Appl. Algebra, 219 (8), pp. 3568-3603
- Bachiller, D., Counterexample to a conjecture about braces (2016) J. Algebra, 453
- Bai, C., Bijective 1-cocycles and classification of 3-dimensional left-symmetric algebras (2009) Comm. Algebra, 37 (3), pp. 1016-1057
- Burde, D., Left-symmetric structures on simple modular Lie algebras (1994) J. Algebra, 169 (1), pp. 112-138
- Burde, D., Left-symmetric algebras, or pre-Lie algebras in geometry and physics (2006) Cent. Eur. J. Math, 4 (3), pp. 323-357
- Cedó, F., Jespers, E., Okniński, J., Braces and the Yang-Baxter equation (2014) Comm. Math. Phys, 327 (1), pp. 101-116
- Drinfel′ d, V.G., On some unsolved problems in quantum group theory, Quantum groups (1990) On some unsolved problems in quantum group theory, 1510, pp. 1-8
- Etingof, P., Schedler, T., Soloviev, A., Set-theoretical solutions to the quantum Yang-Baxter equation (1999) Duke Math. J, 100 (2), pp. 169-209
- Gateva-Ivanova, T., Set-theoretic solutions of the Yang-Baxter equation Braces, and Symmetric Groups, , arXiv:1507.02602, 2015
- Gateva-Ivanova, T., Van Den Bergh, M., Semigroups of I-type (1998) J. Algebra, 206 (1), pp. 97-112
- Green, J.A., Nichols, W.D., Earl, J., Taft, Left Hopf algebras (1980) J. Algebra, 65 (2), pp. 399-411
- Guarnieri, L., Vendramin, L., Skew braces and the Yang-Baxter equation Accepted for Publication in Math. Comp, , arXiv:1511.03171, 2015
- Kassel, C., (1995) Quantum Groups, Graduate Texts in Mathematics, 155. , Springer-Verlag, New York
- Kim, H., Complete left-invariant affine structures on nilpotent Lie groups (1986) J. Differential Geom, 24 (3), pp. 373-394
- Lu, J.-H., Yan, M., Zhu, Y.-C., On the set-theoretical Yang-Baxter equation (2000) Duke Math. J, 104 (1), pp. 1-18
- Perea, A.M., Flat left-invariant connections adapted to the automorphism structure of a Lie group (1982) 16 (1981), 3, pp. 445-474
- Rump, W., Braces, radical rings, and the quantum Yang-Baxter equation (2007) J. Algebra, 307 (1), pp. 153-170
- Rump, W., The brace of a classical group (2014) Note Mat, 34 (1), pp. 115-144
- Smoktunowicz, A., On Engel Groups, Nilpotent Groups, Rings, Braces and the Yang-Baxter Equation, , arXiv:1509.00420, 2015
- Soloviev, A., Non-unitary set-theoretical solutions to the quantum Yang-Baxter equation (2000) Math. Res. Lett, 7 (5-6), pp. 577-596
- William, C., (1979) Waterhouse, Introduction to Affine Group Schemes, Graduate Texts in Mathematics, 66. , Springer-Verlag, New York-Berlin
Citas:
---------- APA ----------
Angiono, I., Galindo, C. & Vendramin, L.
(2017)
. Hopf braces and Yang-Baxter operators. Proceedings of the American Mathematical Society, 145(5), 1981-1995.
http://dx.doi.org/10.1090/proc/13395---------- CHICAGO ----------
Angiono, I., Galindo, C., Vendramin, L.
"Hopf braces and Yang-Baxter operators"
. Proceedings of the American Mathematical Society 145, no. 5
(2017) : 1981-1995.
http://dx.doi.org/10.1090/proc/13395---------- MLA ----------
Angiono, I., Galindo, C., Vendramin, L.
"Hopf braces and Yang-Baxter operators"
. Proceedings of the American Mathematical Society, vol. 145, no. 5, 2017, pp. 1981-1995.
http://dx.doi.org/10.1090/proc/13395---------- VANCOUVER ----------
Angiono, I., Galindo, C., Vendramin, L. Hopf braces and Yang-Baxter operators. Proc. Am. Math. Soc. 2017;145(5):1981-1995.
http://dx.doi.org/10.1090/proc/13395