"Set-theoretical" solutions of the quantum Yang-Baxter equation and a class of Garside groups

Abstract

We establish a one-to-one correspondence between structure groups of non-degenerate, involutive and braided "set-theoretical" solutions of the quantum Yang-Baxter equation and Garside groups with a certain presentation. Moreover, we show that the solution is indecomposable if and only if its structure group is a $\Delta-$pure Garside group.