Folding of set-theoretical solutions of the Yang-Baxter equation

Fabienne Chouraqui (1) , Eddy Godelle (2)

1 Department of Mathematics [Bar-Ilan]
2 LMNO - Laboratoire de Mathématiques Nicolas Oresme

We establish a correspondence between the invariant subsets of a non-degenerate symmetric set-theoretical solution of the quantum Yang-Baxter equation and the parabolic subgroups of its structure group, equipped with its canonical Garside structure. Moreover, we introduce the notion of a foldable solution, which extends the one of a decomposable solution.

Mots clés: set-theoretical solution of the quantum Yang-Baxter equation; parabolic subgroups of Garside groups; folding

Domaines: Théorie des groupes [math.GR]; Algèbres quantiques [math.QA]

Fabienne Chouraqui, Eddy Godelle. Folding of set-theoretical solutions of the Yang-Baxter equation. 2010. ⟨hal-00518243⟩