To every group of I-type, we associate a finite quotient group that plays the role that Coxeter groups play for Artin-Tits groups. Since groups of I-type are examples of Garside groups, this answers a question of D. Bessis in the particular case of groups of I-type. Groups of I-type are related to finite set-theoretical solutions of the Yang-Baxter equation. So, our result provides a new tool to attack the problem of the classification of finite set-theoretical solutions of the Yang-Baxter equation.
Bibliographical noteFunding Information:
Both authors are partially supported by the Agence Nationale de la Recherche (projet Théorie de Garside, ANR-08-BLAN-0269-03 ). The first author was supported by the Israel Science Foundation (n o 580/07 ).
- Garside groups
- Set-theoretical solution of the quantum Yang-Baxter equation
ASJC Scopus subject areas
- Mathematics (all)