Set-theoretical solutions to the Hom-Yang-Baxter equation and Hom-cycle sets

DOI10.1016/j.jalgebra.2023.05.004zbMath1527.16035arXiv2212.00274OpenAlexW4376113429MaRDI QIDQ6169038

Xiankun Du, Kaiqiang Zhang

Publication date: 11 July 2023

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

Full work available at URL: https://arxiv.org/abs/2212.00274

zbMATH Keywords

cycle setHom-Yang-Baxter equationset-theoretic solutionleft quasigroupHom-cycle set

Mathematics Subject Classification ID

Loops, quasigroups (20N05) Sets with a single binary operation (groupoids) (20N02) Yang-Baxter equations (16T25)

Cites Work

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• Homology of left non-degenerate set-theoretic solutions to the Yang-Baxter equation
• Dynamical Yang-Baxter maps associated with homogeneous pre-systems
• Braces, radical rings, and the quatum Yang-Baxter equation.
• Hopf algebroids and rigid tensor categories associated with dynamical Yang-Baxter maps
• Semigroups of \(I\)-type
• Solutions of the quantum dynamical Yang-Baxter equation and dynamical quantum groups
• On the set-theoretical Yang-Baxter equation
• 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
• Dynamical braces and dynamical Yang-Baxter maps
• Set-theoretical solutions to the quantum Yang-Baxter equation
• Solutions of the Hom-Yang-Baxter equation from monoidal Hom-(co)algebra structures
• Indecomposable involutive set-theoretic solutions of the Yang-Baxter equation
• Involutive Latin solutions of the Yang-Baxter equation
• Indecomposable involutive set-theoretic solutions of the Yang-Baxter equation and orthogonal dynamical extensions of cycle sets
• Hom-Tensor categories and the Hom-Yang-Baxter Equation
• Foundations of Garside theory
• Braces and the Yang-Baxter equation
• Matched pairs approach to set theoretic solutions of the Yang-Baxter equation.
• Set-theoretic solutions of the Yang-Baxter equation, RC-calculus, and Garside germs.
• Partition function of the eight-vertex lattice model
• Quiver-theoretical approach to dynamical Yang-Baxter maps
• Dynamical groups and braces
• Skew braces and the Yang–Baxter equation
• Hom-quantum groups: I. Quasi-triangular Hom-bialgebras
• The Hom–Yang–Baxter equation, Hom–Lie algebras, and quasi-triangular bialgebras
• On some unsolved problems in quantum group theory
• A new family of set-theoretic solutions of the Yang–Baxter equation
• On Engel groups, nilpotent groups, rings, braces and the Yang-Baxter equation
• A combinatorial approach to the set-theoretic solutions of the Yang–Baxter equation
• On the indecomposable involutive set-theoretic solutions of the Yang-Baxter equation of prime-power size
• About a question of Gateva-Ivanova and Cameron on square-free set-theoretic solutions of the Yang-Baxter equation
• THE CLASSICAL HOM-YANG-BAXTER EQUATION AND HOM-LIE BIALGEBRAS
• The Hom–Yang–Baxter equation and Hom–Lie algebras
• The category of Yetter-Drinfel'd Hom-modules and the quantum Hom-Yang-Baxter equation
• NOETHERIAN SEMIGROUP ALGEBRAS
• Some Exact Results for the Many-Body Problem in one Dimension with Repulsive Delta-Function Interaction
• Hom-Yang-Baxter equations and Hom-Yang-Baxter systems