A family of solutions of the Yang-Baxter equation.

DOI10.1016/j.jalgebra.2014.05.011zbMath1303.16036arXiv1312.5142OpenAlexW2962849672MaRDI QIDQ403608

David Bachiller, Ferran Cedó

Publication date: 29 August 2014

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1312.5142

zbMATH Keywords

Yang-Baxter equationbracesIYB groupsinvolutive non-degenerate solutions

Mathematics Subject Classification ID

Yang-Baxter equations (16T25)

Related Items (15)

On groups of \(I\)-type and involutive Yang-Baxter groups ⋮ Solutions of the Yang-Baxter equation associated with a left brace. ⋮ Semi-braces and the Yang-Baxter equation ⋮ On Engel groups, nilpotent groups, rings, braces and the Yang-Baxter equation ⋮ On the commuting solutions to the Yang-Baxter-like matrix equation for identity matrix minus special rank-two matrices ⋮ Numerically stable iterative methods for computing matrix sign function ⋮ The interplay between \(k\)-graphs and the Yang-Baxter equation. ⋮ Solving the Yang-Baxter-like matrix equation for a class of elementary matrices ⋮ On the Yang-Baxter-like matrix equation for rank-two matrices ⋮ On commuting solutions of the Yang-Baxter-like matrix equation ⋮ Complete commuting solutions of the Yang-Baxter-like matrix equation for diagonalizable matrices ⋮ Set-theoretic solutions of the Yang-Baxter equation, braces and symmetric groups ⋮ Some non-commuting solutions of the Yang-Baxter-like matrix equation ⋮ The matched product of set-theoretical solutions of the Yang-Baxter equation ⋮ Commuting solutions of the Yang-Baxter-like matrix equation for a class of rank-two updated matrices

Cites Work

• Multipermutation solutions of the Yang-Baxter equation
• Monoids and groups of I-type.
• Braces, radical rings, and the quatum Yang-Baxter equation.
• Semigroups of \(I\)-type
• On the set-theoretical Yang-Baxter equation
• Set-theoretical solutions to the quantum Yang-Baxter equation
• Matched pairs approach to set theoretic solutions of the Yang-Baxter equation.
• Involutive Yang-Baxter groups
• On some unsolved problems in quantum group theory
• A combinatorial approach to the set-theoretic solutions of the Yang–Baxter equation
• NOETHERIAN SEMIGROUP ALGEBRAS
• Some Exact Results for the Many-Body Problem in one Dimension with Repulsive Delta-Function Interaction

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