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

JOURNAL OF ALGEBRA

卷:587

Article

Caranti, A.¹  Stefanello, L.² 

[1] Univ Trento, Dipartimento Matemat, Via Sommarive 14, I-38123 Trento, Italy

[2] Univ Pisa, Dipartimento Matemat, Largo Bruno Pontecorvo 5, I-56127 Pisa, Italy

关键词: Holomorph;    Endomorphisms;    Regular subgroups;    Skew braces;    Yang-Baxter equation;    Hopf-Galois structures;   

DOI  :  10.1016/j.jalgebra.2021.07.029

来源: Elsevier

【 摘 要 】

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, center dot, o) from an endomorphism of a group (G, center dot) whose image is abelian. In this paper, we characterise the endomorphisms of a group (G, center dot) 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. (C) 2021 Elsevier Inc. All rights reserved.

【 授权许可】

Free