Coxeter-like groups for set-theoretic solutions of the Yang–Baxter equation

Patrick Dehornoy

doi:10.1016/j.crma.2013.07.002

Algebra

Coxeter-like groups for set-theoretic solutions of the Yang–Baxter equation

Presented by: the Editorial Board

Patrick Dehornoy ¹

¹ Laboratoire de mathématiques Nicolas-Oresme, CNRS UMR 6139, université de Caen, 14032 Caen cedex, France

Comptes Rendus. Mathématique, Volume 351 (2013) no. 11-12, pp. 419-424.

Abstract (Original language)
Résumé

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.

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.

Received: 2013-05-16
Accepted: 2013-07-03
Published online: 2013-06-01

DOI: 10.1016/j.crma.2013.07.002

Author's affiliations:

Patrick Dehornoy ¹

¹ Laboratoire de mathématiques Nicolas-Oresme, CNRS UMR 6139, université de Caen, 14032 Caen cedex, France

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Patrick Dehornoy. Coxeter-like groups for set-theoretic solutions of the Yang–Baxter equation. Comptes Rendus. Mathématique, Volume 351 (2013) no. 11-12, pp. 419-424. doi : 10.1016/j.crma.2013.07.002. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2013.07.002/

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