Indecomposable involutive solutions of the Yang-Baxter equation of multipermutational level 2 with abelian permutation group

DOI10.1515/forum-2021-0130zbMath1494.16036arXiv2011.00229OpenAlexW3198689339MaRDI QIDQ2121266

Anna Zamojska-Dzienio, Přemysl Jedlička, Agata Pilitowska

Publication date: 4 April 2022

Published in: Forum Mathematicum (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2011.00229

zbMATH Keywords

Yang-Baxter equationtransitive groupmultipermutation solutionset-theoretic solution

Mathematics Subject Classification ID

Subgroups of symmetric groups (20B35) Yang-Baxter equations (16T25)

Related Items (9)

Simplicity of indecomposable set-theoretic solutions of the Yang-Baxter equation ⋮ Cocyclic braces and indecomposable cocyclic solutions of the Yang-Baxter equation ⋮ A characterization of finite simple set-theoretic solutions of the Yang-Baxter equation ⋮ Indecomposable solutions of the Yang-Baxter equation of square-free cardinality ⋮ Indecomposable solutions of the Yang-Baxter equation with permutation group of sizes pq and p ² q ⋮ A note on set theoretical solutions of the Yang-Baxter equation with trivial retraction ⋮ Indecomposable involutive solutions of the Yang-Baxter equation of multipermutation level 2 with non-abelian permutation group ⋮ Indecomposable involutive set-theoretic solutions of the Yang-Baxter equation and orthogonal dynamical extensions of cycle sets ⋮ New simple solutions of the Yang-Baxter equation and solutions associated to simple left braces

Cites Work

• Unnamed Item
• Quantum spaces associated to multipermutation solutions of level two
• Classification of indecomposable involutive set-theoretic solutions to the Yang-Baxter equation
• The retraction relation for biracks
• 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
• Indecomposable involutive set-theoretic solutions of the Yang-Baxter equation
• The construction of multipermutation solutions of the Yang-Baxter equation of level 2
• Braces and the Yang-Baxter equation
• Set-theoretic solutions of the Yang-Baxter equation, graphs and computations
• INTRODUCTION TO THE YANG-BAXTER EQUATION
• On some unsolved problems in quantum group theory
• On the indecomposable involutive set-theoretic solutions of the Yang-Baxter equation of prime-power size
• Problems on skew left braces

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