ALGB Seminar: Leandro Vendramin (Universidad de Buenos Aires) II

10/10/2018 - 16:00

Skew braces and the Yang-Baxter equation

We give an introduction to the theory of skew braces with applications to set-theoretic solutions to the Yang-Baxter equation. Main topics:
Set theoretic solutions and skew braces.  Ideals, series of ideals, left/right nilpotent skew braces.  Prime and semiprime ideals, radicals and solvable skew braces.  Open problems.

References:

1. Cedó, F.; Left braces: solutions of the Yang-Baxter equation. Adv. Group Theory Appl. 5 (2018), 33-90.
2. Cedó, F.; Smoktunowicz, A.; Vendramin, L.; Skew left braces of nilpotent type. preprint arXiv:1806.01127.
3. Cedó, F.; Jespers, E.; Okniński, J.; Braces and the Yang-Baxter equation. Comm. Math. Phys. 327 (2014), no. 1, 101–116.
4. Konovalov, A.; Smoktunowicz, A.; Vendramin, L.; On skew braces and their ideals. Accepted for publication in Exp. Math
5. Guarnieri, L.; Vendramin, L. Skew braces and the Yang-Baxter equation. Math. Comp. 86 (2017), no. 307, 2519–2534.
6. Jespers, E.; Okniński, J.; Noetherian semigroup algebras. Algebra and Applications, 7. Springer, Dordrecht, 2007. x+361 pp.
7. Rump, W.; Braces, radical rings, and the quantum Yang-Baxter equation. J. Algebra 307 (2007), no. 1, 153–170
8. Smoktunowicz, A.; Vendramin, L.; On skew braces (with an appendix by N. Byott and L. Vendramin). J. Comb. Algebra 2 (2018), no. 1, 47–86.