A characterization of finite multipermutation solutions of the Yang-Baxter equation

We prove that a finite non-degenerate involutive set-theoretic solution (X, r) of the Yang-Baxter equation is a multipermutation solution if and only if its structure group G(X, r) admits a left ordering or equivalently it is poly-Z.

Detalles Bibliográficos
Autores: Bachiller Perez, David, Cedó, Ferran|||0000-0003-4703-2782, Vendramin, L.
Tipo de recurso: artículo
Fecha de publicación:2018
País:España
Institución:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:191243
Acceso en línea:https://ddd.uab.cat/record/191243
https://dx.doi.org/urn:doi:10.5565/PUBLMAT6221809
Access Level:acceso abierto
Palabra clave:Yang-Baxter equation
Set-theoretic solution
Brace
Ordered groups
Poly-(infinite cyclic) group
Descripción
Sumario:We prove that a finite non-degenerate involutive set-theoretic solution (X, r) of the Yang-Baxter equation is a multipermutation solution if and only if its structure group G(X, r) admits a left ordering or equivalently it is poly-Z.