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  11.02.2019 - Relation between braces and units of group rings - Seminario di Algebra ARS

Nell’ambito degli incontri di Algebra Reading Seminar, il 13 febbraio 2019, in aula Benvenuti, ore 11.00, Charlotte Verwimp terrà un seminario dal titolo

“Relation between braces and units of group rings”

Abstract: 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.

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