Garside groups and Yang-Baxter equation

Abstract

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 $\Delta$-pure Garside groups.Comment: This is the last version of the paper, as it appears in Communications in Algebra, Volume 38 Issue 12, December 201