Skip to main content Accessibility help
×
×
Home

Left Braces and the Quantum Yang–Baxter Equation

  • H. Meng (a1), A. Ballester-Bolinches (a1) and R. Esteban-Romero (a1)

Abstract

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.

Copyright

Corresponding author

*Corresponding author.

Footnotes

Hide All

Permanent address: Institut Universitari de Matemàtica Pura i Aplicada, Universitat Politècnica de València, Camí de Vera, s/n, 46022 València, Spain, email: resteban@mat.upv.es.

Footnotes

References

Hide All
1.Bachiller, D., Cedó, F. and Jespers, E., Solutions of the Yang–Baxter equation associated with a left brace, J. Algebra 463 (2016), 80102.
2.Cedó, F., Gateva-Ivanova, T. and Smoktunowicz, A., On the Yang–Baxter equation and left nilpotent left braces, J. Pure Appl. Algebra 221(4) (2017), 751756.
3.Cedó, F., Jespers, E. and Okniński, J., Braces and the Yang–Baxter equation, Commun. Math. Phys. 327 (2014), 101116.
4.Etingof, P., Schedler, T. and Soloviev, A., Set theoretical solutions to the quantum Yang–Baxter equation, Duke Math. J. 100 (1999), 169209.
5.Kurzweil, H. and Stellmacher, B., The theory of finite groups. An introduction. Universitext (Springer-Verlag, New York, 2004).
6.Radford, D. E., Hopf algebras (World Scientific, 2012).
7.Rump, W., Braces, radical rings, and the quantum Yang–Baxter equation, J. Algebra 307 (2007), 153170.
8.Smoktunowicz, A., A note on set-theoretic solutions of the Yang–Baxter equation, J. Algebra 500 (2018), 318.
9.Smoktunowicz, A., On Engel groups, nilpotent groups, rings, braces and Yang–Baxter equation, Trans. Amer. Math. Soc. 370 (2018), 65356564.
10.Sysak, Y., Products of groups and local nearrings, Note Mat. 28 (2008), 181216.
11.Yang, C. N., Some exact results for many-body problem in one dimension with repulsive delta-function interaction, Phys. Rev. Lett. 19 (1967), 13121315.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Proceedings of the Edinburgh Mathematical Society
  • ISSN: 0013-0915
  • EISSN: 1464-3839
  • URL: /core/journals/proceedings-of-the-edinburgh-mathematical-society
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×

Keywords

MSC classification

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed