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.

This is the last version of the paper, as it appears in Communications in Algebra, Volume 38 Issue 12, December 2010

References in corpus (3)

• Set-theoretical solutions to the quantum Yang-Baxter equation
• On set-theoretical solutions of the quantum Yang-Baxter equation
• A combinatorial approach to the set-theoretic solutions of the Yang-Baxter equation

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• Left non-degenerate set-theoretic solutions of the Yang-Baxter equation and semitrusses
• Combinatorial solutions to the reflection equation
• Retractability of solutions to the Yang-Baxter equation and $p$-nilpotency of skew braces
• The Yang-Baxter equation and Thompson's group $F$
• Skew braces: a brief survey
• A note on Garside monoids and Braces
• The Yang-Baxter equation, Quantum computing and Quantum entanglement
• Structure groupoids of quiver-theoretic Yang-Baxter maps