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 Δ-pure Garside groups.

Key Words:

• Garside groups
• Monoid presentation
• Quantum Yang–Baxter equations

2000 Mathematics Subject Classification:

• Primary 16T25, 20F05
• Secondary 20F36

ACKNOWLEDGMENTS

This work is a part of the author's Ph.D. research, done at the Technion under the supervision of Professor Arye Juhasz. I am very grateful to Professor Arye Juhasz, for his patience, his encouragement, and his many helpful remarks. I am also grateful to Professor Patrick Dehornoy for his comments on this article.

Notes

Communicated by M. Kambites.