On derived-indecomposable solutions of the Yang-Baxter equation
Colazzo, Ilaria (University of Leeds. School of Mathematics)
Ferrara, Maria (Università degli Studi della Campania "Luigi Vanvitelli". Dipartimento di Matematica e Fisica)
Trombetti, Marco (Universitá degli studi di Napoli Federico II. Dipartimento di Matematica e Applicazioni "R. Caccioppoli")

Date:	2025
Abstract:	If (X, r) is a finite non-degenerate set-theoretic solution of the Yang-Baxter equation, the additive group of the structure skew brace G(X, r) is an F C-group, i. e. a group whose elements have finitely many conjugates. Moreover, its multiplicative group is virtually abelian, so it is also close to being an F C-group itself. If one additionally assumes that the derived solution of (X, r) is indecomposable, then for every element b of G(X, r) there are finitely many elements of the form b∗c and c ∗ b, with c ∈ G(X, r). This naturally leads to the study of a brace-theoretic analogue of the class of F C-groups. For this class of skew braces, the fundamental results and their connections with the solutions of the YBE are described: we prove that they have good torsion and radical theories, and that they behave well with respect to certain nilpotency concepts and finite generation.
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Language:	Anglès
Document:	Article ; recerca ; Versió publicada
Subject:	Yang-Baxter equation ; Indecomposable solution ; Skew brace ; F c-group
Published in:	Publicacions matemàtiques, Vol. 69 Núm. 1 (2025) , p. 171-193 (Articles) , ISSN 2014-4350

Adreça original: https://raco.cat/index.php/PublicacionsMatematiques/article/view/433286
DOI: 10.5565/PUBLMAT6912508

23 p, 423.3 KB

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