Semi-braces and the Yang-Baxter equation

DOI10.1016/j.jalgebra.2017.03.035zbMath1385.16035OpenAlexW2606599669MaRDI QIDQ2397554

Paola Stefanelli, Francesco Catino, Ilaria Colazzo

Publication date: 22 May 2017

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

Full work available at URL: https://doi.org/10.1016/j.jalgebra.2017.03.035

zbMATH Keywords

quantum Yang-Baxter equationsemi-braceset-theoretical solutionskew brace

Mathematics Subject Classification ID

Quantum groups and related algebraic methods applied to problems in quantum theory (81R50) Jacobson radical, quasimultiplication (16N20) Generalizations (16Y99) Yang-Baxter equations (16T25)

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Cites Work

• Unnamed Item
• Unnamed Item
• Regular subgroups of the affine group and asymmetric product of radical braces.
• A family of solutions of the Yang-Baxter equation.
• Braces, radical rings, and the quatum Yang-Baxter equation.
• Semigroups of \(I\)-type
• Another solution of Yang-Baxter equation on set and ``metahomomorphisms on groups
• On the set-theoretical Yang-Baxter equation
• Dynamical braces and dynamical Yang-Baxter maps
• Set-theoretical solutions to the quantum Yang-Baxter equation
• Classification of braces of order \(p^3\)
• Braces and the Yang-Baxter equation
• Partition function of the eight-vertex lattice model
• Skew braces and the Yang–Baxter equation
• On some unsolved problems in quantum group theory
• ON REGULAR SUBGROUPS OF THE AFFINE GROUP
• Some Exact Results for the Many-Body Problem in one Dimension with Repulsive Delta-Function Interaction
• Non-unitary set-theoretical solutions to the quantum Yang-Baxter equation.

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