Coxeter-like groups for set-theoretic solutions of the Yang-Baxter equation.

DOI10.1016/J.CRMA.2013.07.002zbMath1286.20042arXiv1305.3900OpenAlexW2019163314MaRDI QIDQ367175

Patrick Dehornoy

Publication date: 26 September 2013

Published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1305.3900

zbMATH Keywords

Yang-Baxter equationsmonoid presentationsset-theoretic solutionsGarside groups

Mathematics Subject Classification ID

Quantum groups and related algebraic methods applied to problems in quantum theory (81R50) Braid groups; Artin groups (20F36) Yang-Baxter equations (16T25)

Related Items (7)

Left orders in Garside groups ⋮ A new family of set-theoretic solutions of the Yang–Baxter equation ⋮ Extensions of set-theoretic solutions of the Yang-Baxter equation and a conjecture of Gateva-Ivanova. ⋮ On some Garsideness properties of structure groups of set-theoretic solutions of the Yang-Baxter equation ⋮ The Yang–Baxter equation and Thompson’s group F ⋮ Finite quotients of groups of I-type. ⋮ An algorithmic construction of group automorphisms and the quantum Yang-Baxter equation

Cites Work

• Garside families and Garside germs
• Monoids and groups of I-type.
• Semigroups of \(I\)-type
• A decomposition theorem for square-free unitary solutions of the quantum Yang-Baxter equation
• Set-theoretical solutions to the quantum Yang-Baxter equation
• Finite quotients of groups of I-type.
• Garside Groups and Yang–Baxter Equation
• Groupes de Garside
• NOETHERIAN SEMIGROUP ALGEBRAS

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