The construction of multipermutation solutions of the Yang-Baxter equation of level 2

DOI10.1016/j.jcta.2020.105295zbMath1458.16041arXiv1901.01471OpenAlexW3043098117MaRDI QIDQ2194762

Anna Zamojska-Dzienio, Přemysl Jedlička, Agata Pilitowska

Publication date: 7 September 2020

Published in: Journal of Combinatorial Theory. Series A (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1901.01471

zbMATH Keywords

Yang-Baxter equationrackbirackmultipermutation solutionleft distributivityset-theoretic solutionone-sided quasigroup

Mathematics Subject Classification ID

Yang-Baxter equations (16T25)

Related Items (13)

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 ⋮ On the indecomposable involutive set-theoretic solutions of the Yang-Baxter equation of prime-power size ⋮ On bi-skew braces and brace blocks ⋮ Skew left braces and 2-reductive solutions of the Yang-Baxter equation ⋮ A note on set theoretical solutions of the Yang-Baxter equation with trivial retraction ⋮ From braces to pre-Lie rings ⋮ Involutive Latin solutions of the Yang-Baxter equation ⋮ Indecomposable involutive solutions of the Yang-Baxter equation of multipermutation level 2 with non-abelian permutation group ⋮ Quandles with orbit series conditions ⋮ Constructing finite simple solutions of the Yang-Baxter equation ⋮ Indecomposable involutive set-theoretic solutions of the Yang-Baxter equation and orthogonal dynamical extensions of cycle sets ⋮ Two theorems on balanced braces

Uses Software

• Prover9
• Mace4
• OEIS

Cites Work

• Enumerating finite racks, quandles and kei
• The structure of medial quandles
• Quantum spaces associated to multipermutation solutions of level two
• Multipermutation solutions of the Yang-Baxter equation
• Equational theories of medial groupoids
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• Retractability of set theoretic solutions of the Yang-Baxter equation
• Reductive modes
• Braids and self-distributivity
• The retraction relation for biracks
• Biquandles and virtual links
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• Set-theoretic solutions of the Yang-Baxter equation, braces and symmetric groups
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• A Survey of Quandle Ideas
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• INTRODUCTION TO THE YANG-BAXTER EQUATION
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• On some unsolved problems in quantum group theory
• RACKS AND LINKS IN CODIMENSION TWO
• A combinatorial approach to the set-theoretic solutions of the Yang–Baxter equation
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