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.
Accepted:
Published online:
Patrick Dehornoy 1
@article{CRMATH_2013__351_11-12_419_0, author = {Patrick Dehornoy}, title = {Coxeter-like groups for set-theoretic solutions of the {Yang{\textendash}Baxter} equation}, journal = {Comptes Rendus. Math\'ematique}, pages = {419--424}, publisher = {Elsevier}, volume = {351}, number = {11-12}, year = {2013}, doi = {10.1016/j.crma.2013.07.002}, language = {en}, }
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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