"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.

References in corpus (3)

• Set-theoretical solutions to the quantum Yang-Baxter equation
• On set-theoretical solutions of the quantum Yang-Baxter equation
• Semigroups of I-type

Cited by in corpus (2)

• Finite dimensional Hopf actions on central division algebras
• Garside structure on monoids with quadratic square-free relations