Left Braces: Solutions of the Yang-Baxter Equation

Autor: Ferran Cedó

Publikováno v: Advances in Group Theory and Applications, Vol 5, Pp 33-90 (2018)

This is a survey on the theory of left braces, an algebraic structure introduced by Rump as a generalization of Jacobson radical rings to study non-degenerate involutive set-theoretic solutions of the Yang-Baxter equation.

Externí odkaz: https://doaj.org/article/85318b485c204fccb1725616465b0ff0

Set-theoretic solutions of the Yang–Baxter equation, associated quadratic algebras and the minimality condition

Autor: Ferran Cedó, Eric Jespers, Jan Okniński

Publikováno v: Revista Matemática Complutense. 34:99-129

Given a finite non-degenerate set-theoretic solution $(X,r)$ of the Yang-Baxter equation and a field $K$, the structure $K$-algebra of $(X,r)$ is $A=A(K,X,r)=K\langle X\mid xy=uv \mbox{ whenever }r(x,y)=(u,v)\rangle$. Note that $A=\oplus_{n\geq 0} A_

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::66cce0e4b25b50f843d502b06d1caa14
https://doi.org/10.1007/s13163-019-00347-6

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

Autor: Ferran Cedó, Leandro Vendramin, David Bachiller

Publikováno v: Recercat: Dipósit de la Recerca de Catalunya
Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
Recercat. Dipósit de la Recerca de Catalunya
instname
Publicacions Matemàtiques; Vol. 62, Núm. 2 (2018); p. 641–649
CONICET Digital (CONICET)
Consejo Nacional de Investigaciones Científicas y Técnicas
instacron:CONICET
Dipòsit Digital de Documents de la UAB
Universitat Autònoma de Barcelona
Publ. Mat. 62, no. 2 (2018), 641-649

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-(infinite cyclic).