We establish a one-to-one correspondence between a class of Garside groups admitting a certain presentation and the structure groups of non-degenerate, involutive, and braided set-theoretical solutions of the quantum Yang-Baxter equation. We also characterize indecomposable solutions in terms of Δ-pure Garside groups.
- Garside groups
- Monoid presentation
- Quantum Yang-Baxter equations
ASJC Scopus subject areas
- Algebra and Number Theory