Retractability of solutions to the Yang-Baxter equation and p-nilpotency of skew braces
Using Bieberbach groups, we study multipermutation involutive solutions to the Yang-Baxter equation. We use a linear representation of the structure group of an involutive solution to study the unique product property in such groups. An algorithm to find subgroups of a Bieberbach group isomorphic to...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2019 |
| País: | Argentina |
| Institución: | Consejo Nacional de Investigaciones Científicas y Técnicas |
| Repositorio: | CONICET Digital (CONICET) |
| Idioma: | inglés |
| OAI Identifier: | oai:ri.conicet.gov.ar:11336/136766 |
| Acceso en línea: | http://hdl.handle.net/11336/136766 |
| Access Level: | acceso abierto |
| Palabra clave: | BIEBERBACH GROUP MULTIPERMUTATION SOLUTION SET-THEORETIC SOLUTION SKEW BRACE UNIQUE PRODUCT PROPERTY YANG-BAXTER EQUATION https://purl.org/becyt/ford/1.1 https://purl.org/becyt/ford/1 |
| Sumario: | Using Bieberbach groups, we study multipermutation involutive solutions to the Yang-Baxter equation. We use a linear representation of the structure group of an involutive solution to study the unique product property in such groups. An algorithm to find subgroups of a Bieberbach group isomorphic to the Promislow subgroup is introduced and then used in the case of structure group of involutive solutions. To extend the results related to retractability to non-involutive solutions, following the ideas of Meng, Ballester-Bolinches and Romero, we develop the theory of right p-nilpotent skew braces. The theory of left p-nilpotent skew braces is also developed and used to give a short proof of a theorem of Smoktunowicz in the context of skew braces. |
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