Factorizations of skew braces
We introduce strong left ideals of skew braces and prove that they produce non-trivial decomposition of set-theoretic solutions of the Yang–Baxter equation. We study factorization of skew left braces through strong left ideals and we prove analogs of Itô’s theorem in the context of skew left braces....
| Autores: | , , , |
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| Formato: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2019 |
| País: | Argentina |
| Recursos: | Consejo Nacional de Investigaciones Científicas y Técnicas |
| Repositorio: | CONICET Digital (CONICET) |
| Idioma: | inglés |
| OAI Identifier: | oai:ri.conicet.gov.ar:11336/136170 |
| Acesso em linha: | http://hdl.handle.net/11336/136170 |
| Access Level: | acceso abierto |
| Palavra-chave: | FACTORIZATION YANG-BAXTER BRACE RADICAL RING https://purl.org/becyt/ford/1.1 https://purl.org/becyt/ford/1 |
| Resumo: | We introduce strong left ideals of skew braces and prove that they produce non-trivial decomposition of set-theoretic solutions of the Yang–Baxter equation. We study factorization of skew left braces through strong left ideals and we prove analogs of Itô’s theorem in the context of skew left braces. As a corollary, we obtain applications to the retractability problem of involutive non-degenerate solutions of the Yang–Baxter equation. Finally, we classify skew braces that contain no non-trivial proper characteristic ideals. |
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