no. 11-12
Algebra
Coxeter-like groups for set-theoretic solutions of the Yang–Baxter equation
[Analogues des groupes de Coxeter pour les solutions ensemblistes de lʼéquation de Yang–Baxter]

Présenté par : the Editorial Board

Dehornoy, Patrick1
1 Laboratoire de mathématiques Nicolas-Oresme, CNRS UMR 6139, université de Caen, 14032 Caen cedex, France
Comptes Rendus. Mathématique, Tome 351 (2013) no. 11-12, pp. 419-424.

On associe à chaque solution ensembliste involutive et non dégénérée de lʼéquation de Yang–Baxter un groupe fini qui joue, pour le groupe de structure associé, le rôle que joue un groupe de Coxeter fini pour le groupe dʼArtin–Tits associé.

We attach with every finite, involutive, nondegenerate set-theoretic solution of the Yang–Baxter equation a finite group that plays for the associated structure group the role that a finite Coxeter group plays for the associated Artin–Tits group.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2013.07.002
Dehornoy, Patrick 1

1 Laboratoire de mathématiques Nicolas-Oresme, CNRS UMR 6139, université de Caen, 14032 Caen cedex, France 
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Dehornoy, Patrick. Coxeter-like groups for set-theoretic solutions of the Yang–Baxter equation. Comptes Rendus. Mathématique, Tome 351 (2013) no. 11-12, pp. 419-424. doi : 10.1016/j.crma.2013.07.002. http://www.numdam.org/articles/10.1016/j.crma.2013.07.002/

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