Aspects of the Category SKB of Skew Braces

DOI10.1080/00927872.2022.2151609zbMATH Open1521.16020arXiv2205.04171MaRDI QIDQ6398603

Alberto Facchini, Dominique Bourn, Unnamed Author

Publication date: 9 May 2022

Abstract: We examine the pointed protomodular category SKB of left skew braces. We study the notion of commutator of ideals in a left skew brace. Notice that in the literature, "product" of ideals of skew braces is often considered. We show that Huq=Smith for left skew braces. Finally, we give a set of generators for the commutator of two ideals, and prove that every ideal of a left skew brace has a centralizer.

Mathematics Subject Classification ID

Yang-Baxter equations (16T25) Other generalizations of groups (20N99) Protomodular categories, semi-abelian categories, Mal'tsev categories (18E13)

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