Skew left braces with non-trivial annihilator

DOI10.1142/S0219498819500336zbMath1447.16035OpenAlexW2789278181MaRDI QIDQ5377484

Francesco Catino, Ilaria Colazzo, Paola Stefanelli

Publication date: 24 May 2019

Published in: Journal of Algebra and Its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0219498819500336

zbMATH Keywords

quantum Yang-Baxter equationaffine groupregular subgroupbraceset-theoretical solutionskew brace\(F\)-braceideal extension of skew braces

Mathematics Subject Classification ID

Quantum groups and related algebraic methods applied to problems in quantum theory (81R50) Primitive groups (20B15) Jacobson radical, quasimultiplication (16N20) Yang-Baxter equations (16T25)

Related Items (20)

Set-theoretic solutions to the Yang-Baxter equation and generalized semi-braces ⋮ The construction of braided tensor categories from Hopf braces ⋮ Nilpotency in left semi-braces ⋮ Set-theoretic solutions of the Yang-Baxter equation associated to weak braces ⋮ Inverse semi-braces and the Yang-Baxter equation ⋮ The matched product of the solutions to the Yang-Baxter equation of finite order ⋮ Left non-degenerate set-theoretic solutions of the Yang–Baxter equation and dynamical extensions of q-cycle sets ⋮ Module braces: relations between the additive and the multiplicative groups ⋮ Extensions and automorphisms of Rota-Baxter groups ⋮ Extensions and Well’s type exact sequence of skew braces ⋮ Central nilpotency of skew braces ⋮ Isoclinism of skew braces ⋮ The algebraic structure of left semi-trusses ⋮ Schur covers of skew braces ⋮ The Yang–Baxter equation and Thompson’s group F ⋮ The structure skew brace associated with a finite non-degenerate solution of the Yang-Baxter equation is finitely presented ⋮ Hopf Galois structures on field extensions of degree twice an odd prime square and their associated skew left braces ⋮ Radical and weight of skew braces and their applications to structure groups of solutions of the Yang-Baxter equation ⋮ Rota-Baxter groups, skew left braces, and the Yang-Baxter equation ⋮ The matched product of set-theoretical solutions of the Yang-Baxter equation

Cites Work

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• Semigroups of \(I\)-type
• On the set-theoretical Yang-Baxter equation
• Extensions, matched products, and simple braces
• Set-theoretical solutions to the quantum Yang-Baxter equation
• Semi-braces and the Yang-Baxter equation
• Braces and the Yang-Baxter equation
• Skew braces and the Yang–Baxter equation
• REGULAR SUBGROUPS OF THE AFFINE GROUP AND RADICAL CIRCLE ALGEBRAS
• On some unsolved problems in quantum group theory
• ON REGULAR SUBGROUPS OF THE AFFINE GROUP
• Non-unitary set-theoretical solutions to the quantum Yang-Baxter equation.
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