The interplay between set-theoretic solutions of the Yang– Baxter equation of Mathematical Physics, skew braces, regular subgroups, and Hopf–Galois structures has spawned a considerable body of literature in recent years. In a recent paper, Alan Koch generalised a construction of Lindsay N. Childs, showing how one can obtain bi-skew braces (G, ·, ◦) from an endomorphism of a group (G, ·) whose image is abelian. In this paper, we characterise the endomorphisms of a group (G, ·) for which Koch’s construction, and a variation on it, yield (bi-)skew braces. We show how the set-theoretic solutions of the Yang–Baxter equation derived by Koch’s construction carry over to our more general situation, and discuss the related Hopf–Galois structures

From endomorphisms to bi-skew braces, regular subgroups, the Yang–Baxter equation, and Hopf–Galois structures / Caranti, A.; Stefanello, L.. - In: JOURNAL OF ALGEBRA. - ISSN 0021-8693. - STAMPA. - 587:(2021), pp. 462-487. [10.1016/j.jalgebra.2021.07.029]

From endomorphisms to bi-skew braces, regular subgroups, the Yang–Baxter equation, and Hopf–Galois structures

Caranti, A.;
2021

Abstract

The interplay between set-theoretic solutions of the Yang– Baxter equation of Mathematical Physics, skew braces, regular subgroups, and Hopf–Galois structures has spawned a considerable body of literature in recent years. In a recent paper, Alan Koch generalised a construction of Lindsay N. Childs, showing how one can obtain bi-skew braces (G, ·, ◦) from an endomorphism of a group (G, ·) whose image is abelian. In this paper, we characterise the endomorphisms of a group (G, ·) for which Koch’s construction, and a variation on it, yield (bi-)skew braces. We show how the set-theoretic solutions of the Yang–Baxter equation derived by Koch’s construction carry over to our more general situation, and discuss the related Hopf–Galois structures
Caranti, A.; Stefanello, L.
From endomorphisms to bi-skew braces, regular subgroups, the Yang–Baxter equation, and Hopf–Galois structures / Caranti, A.; Stefanello, L.. - In: JOURNAL OF ALGEBRA. - ISSN 0021-8693. - STAMPA. - 587:(2021), pp. 462-487. [10.1016/j.jalgebra.2021.07.029]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11572/315484
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