Cohomology, extensions and automorphisms of skew braces

Nishant,; Yadav, Manoj K.

doi:10.1016/j.jpaa.2023.107462

Journal of Pure and Applied Algebra

2024

DOI: 10.1016/j.jpaa.2023.107462

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Cohomology, extensions and automorphisms of skew braces

Nishant Nishant

Manoj K. Yadav

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Cited by 6 publications

References 27 publications

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Solutions of the Yang–Baxter Equation and Strong Semilattices of Skew Braces

Catino,

Mazzotta,

Stefanelli

2024

Mediterr. J. Math.

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We prove that any set-theoretic solution of the Yang–Baxter equation associated with a dual weak brace is a strong semilattice of non-degenerate bijective solutions. This fact makes use of the description of any dual weak brace S we provide in terms of strong semilattice Y of skew braces $$B_\alpha $$ B α , with $$\alpha \in Y$$ α ∈ Y . Additionally, we describe the ideals of S and study its nilpotency by correlating it to that of each skew brace $$B_\alpha $$ B α .

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Solutions of the Yang–Baxter Equation and Strong Semilattices of Skew Braces

Catino,

Mazzotta,

Stefanelli

2024

Mediterr. J. Math.

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show abstract

Cohomology and extensions of relative Rota–Baxter groups

Belwal,

Rathee,

Singh

2025

Journal of Geometry and Physics

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Extensions and automorphisms of Rota-Baxter groups

Das,

Rathee

2023

Journal of Algebra

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Cohomology, extensions and automorphisms of skew braces

Cited by 6 publications

References 27 publications

Solutions of the Yang–Baxter Equation and Strong Semilattices of Skew Braces

Solutions of the Yang–Baxter Equation and Strong Semilattices of Skew Braces

Cohomology and extensions of relative Rota–Baxter groups

Extensions and automorphisms of Rota-Baxter groups

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