Relation between braces and units of group rings

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February 13, 2019
11.00 – 13.00 – Aula Benvenuti
Charlotte Verwimp

Finding solutions of the Yang-Baxter equation has been the subject of many studies in pure mathematics and theoretical physics. In particular, as proposed by Drinfeld [1], the study of set-theoretic solutions has been very attractive over the past few years. One of the tools to study these solutions, called braces, were introduced by Rump [2]. In this talk, we want to show another useful application of braces. In particular we describe a relation between braces and units of group rings [3]. In joint work with Lukasz Kubat, we try to generalize this result for skew braces, a generalization of braces. To do so, we define group near-rings, a generalization of group rings.

[1] V.G. Drinfeld. On some unsolved problems in quantum group theory. Lecture Notes in Math, 1510:1-8, 1992.
[2] W. Rump. Braces, radical rings, and the quantum Yang-Baxter equation. J. Algebra, 307:153-170, 2007.
[3] Y.P. Sysak. Product of groups and the quantum Yang-Baxter equation. Notes of a talk in Advances in Group Theory and Applications, 2011, Porto Cesareo.