New simple solutions of the Yang-Baxter equation and solutions associated to simple left braces

DOI10.1016/j.jalgebra.2022.02.011zbMath1495.16031arXiv2112.07271OpenAlexW4200635431MaRDI QIDQ2118938

Ferran Cedó, Okniński, Jan

Publication date: 23 March 2022

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

Full work available at URL: https://arxiv.org/abs/2112.07271

zbMATH Keywords

Yang-Baxter equationbraceset-theoretic solutionsimple solution

Mathematics Subject Classification ID

Solvable groups, supersolvable groups (20F16) Primitive groups (20B15) Yang-Baxter equations (16T25)

Related Items (3)

A characterization of finite simple set-theoretic solutions of the Yang-Baxter equation ⋮ Indecomposable solutions of the Yang-Baxter equation of square-free cardinality ⋮ On the passage from finite braces to pre-Lie rings

Cites Work

• Unnamed Item
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• Regular subgroups of the affine group and asymmetric product of radical braces.
• Classification of indecomposable involutive set-theoretic solutions to the Yang-Baxter equation
• Braces, radical rings, and the quatum Yang-Baxter equation.
• Extensions of set-theoretic solutions of the Yang-Baxter equation and a conjecture of Gateva-Ivanova.
• Semigroups of \(I\)-type
• Lectures on algebraic quantum groups
• A characterization of finite multipermutation solutions of the Yang-Baxter equation
• Set-theoretic solutions of the Yang-Baxter equation and new classes of \(\mathrm{R}\)-matrices
• A decomposition theorem for square-free unitary solutions of the quantum Yang-Baxter equation
• Set-theoretic solutions of the Yang-Baxter equation, braces and symmetric groups
• Set-theoretical solutions to the quantum Yang-Baxter equation
• An abundance of simple left braces with abelian multiplicative Sylow subgroups
• Indecomposable involutive set-theoretic solutions of the Yang-Baxter equation
• Indecomposable involutive solutions of the Yang-Baxter equation of multipermutational level 2 with abelian permutation group
• Mini-workshop: Algebraic tools for solving the Yang-Baxter equation. Abstracts from the mini-workshop held November 10--16, 2019
• Constructing finite simple solutions of the Yang-Baxter equation
• Braces and the Yang-Baxter equation
• Partition function of the eight-vertex lattice model
• On some unsolved problems in quantum group theory
• On Engel groups, nilpotent groups, rings, braces and the Yang-Baxter equation
• Iterated matched products of finite braces and simplicity; new solutions of the Yang-Baxter equation
• Left Braces: Solutions of the Yang-Baxter Equation
• On the indecomposable involutive set-theoretic solutions of the Yang-Baxter equation of prime-power size
• Asymmetric product of left braces and simplicity; new solutions of the Yang–Baxter equation
• Some Exact Results for the Many-Body Problem in one Dimension with Repulsive Delta-Function Interaction

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