On derived-indecomposable solutions of the Yang-Baxter equation
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...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2025 |
| País: | España |
| Institución: | Universitat Autònoma de Barcelona |
| Repositorio: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglés |
| OAI Identifier: | oai:ddd.uab.cat:304458 |
| Acceso en línea: | https://ddd.uab.cat/record/304458 https://dx.doi.org/urn:doi:10.5565/PUBLMAT6912508 |
| Access Level: | acceso abierto |
| Palabra clave: | Yang-Baxter equation Indecomposable solution Skew brace F c-group |
| Sumario: | 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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