Involutive latin solutions of the Yang Baxter equation

Marco Bonatto (UBA-CONICET)

Lunes 16 de Diciembre, 14.30hs. Aula 27

Wolfgang Rump showed that there is a one-to-one correspondence between nondegenerate involutive set-theoretic solutions of the Yang-Baxter equation and binary algebras in which all left translations $L_x$ are bijections, the squaring map is a bijection, and the identity $(xy)(xz) = (yx)(yz)$ holds. We call these algebras rumples in analogy with quandles, another class of binary algebras giving solutions of the Yang-Baxter equation. We focus on latin rumples, that is, on rumples in which all right translations are bijections as well. In particular, we study the family of affine solutions and their extension theory. We develop the extension theory of rumples sufficiently to obtain examples of latin rumples that are not affine,
not even isotopic to a group.

Joint work with M. Kinyion, D. Stanovsky and P. Vojtechovsky