The retraction relation for biracks

DOI10.1016/J.JPAA.2018.11.020zbMath1411.16032arXiv1808.03302OpenAlexW2887150734MaRDI QIDQ1739190

Přemysl Jedlička, Agata Pilitowska, Anna Zamojska-Dzienio

Publication date: 25 April 2019

Published in: Journal of Pure and Applied Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1808.03302

zbMATH Keywords

Yang-Baxter equationbirackset-theoretical solutioncongruence of an algebraone-sided quasigroupretraction of a solution

Mathematics Subject Classification ID

Subalgebras, congruence relations (08A30) Finitary algebras (08A62) Sets with a single binary operation (groupoids) (20N02) Yang-Baxter equations (16T25)

Related Items (13)

Indecomposable involutive solutions of the Yang-Baxter equation of multipermutational level 2 with abelian permutation group ⋮ Simplicity of indecomposable set-theoretic solutions of the Yang-Baxter equation ⋮ Left non-degenerate set-theoretic solutions of the Yang–Baxter equation and dynamical extensions of q-cycle sets ⋮ On the indecomposable involutive set-theoretic solutions of the Yang-Baxter equation of prime-power size ⋮ The construction of multipermutation solutions of the Yang-Baxter equation of level 2 ⋮ From braces to Hecke algebras and quantum groups ⋮ About a question of Gateva-Ivanova and Cameron on square-free set-theoretic solutions of the Yang-Baxter equation ⋮ Skew left braces and 2-reductive solutions of the Yang-Baxter equation ⋮ Set-theoretic Yang-Baxter \& reflection equations and quantum group symmetries ⋮ Distributive biracks and solutions of the Yang–Baxter equation ⋮ Retractability of solutions to the Yang–Baxter equation and p-nilpotency of skew braces ⋮ A new formula for Lazard's correspondence for finite braces and pre-Lie algebras ⋮ On the passage from finite braces to pre-Lie rings

Uses Software

• Prover9
• Mace4

Cites Work

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