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10 p, 277.5 KB

Corrigendum and addendum to "Structure monoids of set-theoretic solutions of the Yang-Baxter equation" / Cedó, Ferran (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Jespers, Eric (rije Universiteit Brussel. Department of Mathematics) ; Verwimp, Charlotte (Vrije Universiteit Brussel. Department of Mathematics)
One of the results in our article which appeared in Publ. Mat. 65(2) (2021), 499-528,vis that the structure monoid M(X, r) of a left non-degenerate solution (X, r) of the Yang-Baxtervequation is a left semi-truss, in the sense of Brzezi'nski, with an additive structure monoid that is close to being a normal semigroup. [...]
2024 - DOI (Digital Object Identifier)

10.5565/PUBLMAT6812410
Publicacions matemàtiques, Vol. 68 Núm. 1 (2024) , p. 241-250 (Articles)

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30 p, 394.0 KB

Structure monoids of set-theoretic solutions of the Yang-Baxter equation / Cedó, Ferran (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Jespers, Eric (Vrije Universiteit Brussel. Department of Mathematics) ; Vermwimp, Charlotte (Vrije Universiteit Brussel. Department of Mathematics)
Given a set-theoretic solution (X, r) of the Yang-Baxter equation, we denote by M = M(X, r) the structure monoid and by A = A(X, r), respectively A0 = A0 (X, r), the left, respectively right, derived structure monoid of (X, r). [...]
2021 - DOI (Digital Object Identifier)

10.5565/PUBLMAT6522104
Publicacions matemàtiques, Vol. 65 Núm. 2 (2021) , p. 499-528 (Articles)

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9 p, 295.9 KB

A characterization of finite multipermutation solutions of the Yang-Baxter equation / Bachiller Pérez, David (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Cedó, Ferran (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Vendramin, L. (Universidad de Buenos Aires. Departamento de Matemática)
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.
2018 - DOI (Digital Object Identifier)

10.5565/PUBLMAT6221809
Publicacions matemàtiques, Vol. 62 Núm. 2 (2018) , p. 641-649 (Articles)

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25 p, 363.8 KB

Nilpotent groups of class three and braces / Cedó, Ferran (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Jespens, Eric (Vrije Universiteit Brussel. Department of Mathematics) ; Okniński, Jan (Warsaw University (Polònia). Institute of Mathematics)
New constructions of braces on finite nilpotent groups are given and hence this leads to new solutions of the Yang-Baxter equation. In particular, it follows that if a group G of odd order is nilpotent of class three, then it is a homomorphic image of the multiplicative group of a finite left brace (i. [...]
2016 - DOI (Digital Object Identifier)

10.5565/PUBLMAT_60116_03
Publicacions matemàtiques, Vol. 60 Núm. 1 (2016) , p. 55-79 (Survey)

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