On the indecomposable involutive solutions of the Yang-Baxter equation of finite primitive level

In this paper, we study the class of indecomposable involutive solutions of the Yang-Baxter equation of finite primitive level, recently introduced by Cedó and Okninski in [13]. We give a group-theoretic characterization of these solutions by means of displacement groups, and we apply this result to...

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Detalles Bibliográficos
Autor: Castelli, Marco
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:318138
Acceso en línea:https://ddd.uab.cat/record/318138
https://dx.doi.org/urn:doi:10.5565/PUBLMAT6922509
Access Level:acceso abierto
Palabra clave:Imprimitive group
Yang-Baxter equation
Brace
Cycle set
Descripción
Sumario:In this paper, we study the class of indecomposable involutive solutions of the Yang-Baxter equation of finite primitive level, recently introduced by Cedó and Okninski in [13]. We give a group-theoretic characterization of these solutions by means of displacement groups, and we apply this result to compute and enumerate those having small size. For some classes of indecomposable involutive solutions recently studied in the literature, we compute the exact value of the primitive level. Some relationships with other families of solutions are also discussed. Finally, following [13, Question 3.2], we provide a complete description of those having primitive level 2 by left braces.