We establish a correspondence between the invariant subsets of a nondegenerate 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.
Bibliographical noteFunding Information:
Fabienne Chouraqui and Eddy Godelle are partially supported by the Agence Nationale de la Recherche (projet Théorie de Garside, ANR-08-BLAN-0269-03). Fabienne Chouraqui is also supported by the Affdu-Elsevier fellowship.
- Parabolic subgroups of Garside groups
- Set-theoretical solution of the quantum Yang-Baxter equation
ASJC Scopus subject areas
- Mathematics (all)