Indecomposable solutions of the Yang-Baxter equation of square-free cardinality

DOI10.1016/j.aim.2023.109221arXiv2212.06753MaRDI QIDQ6135875

Okniński, Jan, Ferran Cedó

Publication date: 28 August 2023

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2212.06753

zbMATH Keywords

Yang-Baxter equationindecomposable solutionbracemultipermutation solutionset-theoretic solution

Mathematics Subject Classification ID

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

Related Items (3)

The generalization of strong anisotropic XXZ model and UC hierarchy ⋮ Finite skew braces of square-free order and supersolubility ⋮ (In)decomposability of finite solutions of the Yang-Baxter equation

Cites Work

• Unnamed Item
• Unnamed Item
• Multipermutation solutions of the Yang-Baxter equation
• 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
• A characterization of finite multipermutation solutions of the Yang-Baxter equation
• A note on set-theoretic 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-theoretical solutions to the quantum Yang-Baxter equation
• Indecomposable involutive set-theoretic solutions of the Yang-Baxter equation
• New simple solutions of the Yang-Baxter equation and solutions associated to simple left braces
• Indecomposable involutive solutions of the Yang-Baxter equation of multipermutational level 2 with abelian permutation group
• Classification of non-degenerate involutive set-theoretic solutions to the Yang-Baxter equation with multipermutation level two
• Constructing finite simple solutions of the Yang-Baxter equation
• Braces and the Yang-Baxter equation
• Partition function of the eight-vertex lattice model
• Solutions of the Yang-Baxter equation associated with a left brace.
• On various types of nilpotency of the structure monoid and group of a set-theoretic solution of the Yang-Baxter equation
• On some unsolved problems in quantum group theory
• Left Braces: Solutions of the Yang-Baxter Equation
• One-generator braces and indecomposable set-theoretic solutions to the Yang–Baxter equation
• Primitive set-theoretic solutions of the Yang–Baxter equation
• Decomposition Theorems for Involutive Solutions to the Yang–Baxter Equation
• Cocyclic braces and indecomposable cocyclic solutions of the Yang-Baxter equation
• On the indecomposable involutive set-theoretic solutions of the Yang-Baxter equation of prime-power size
• Some Exact Results for the Many-Body Problem in one Dimension with Repulsive Delta-Function Interaction
• Endliche Gruppen I
• A Criterion for Decomposabilty in QYBE
• Indecomposable solutions of the Yang-Baxter equation with permutation group of sizes pq and p ² q

This page was built for publication: Indecomposable solutions of the Yang-Baxter equation of square-free cardinality