On the indecomposable involutive solutions of the Yang-Baxter equation of finite primitive level
Castelli, Marco (Università del Salento (Lecce, Itàlia). Dipartimento di Matematica e Fisica "Ennio De Giorgi")

Date:	2025
Abstract:	In this paper, we study the class of indecomposable involutive solutions of the Yang-Baxter equation of finite primitive level, recently introduced by Cedó and Okninski in [13]. We give a group-theoretic characterization of these solutions by means of displacement groups, and we apply this result to compute and enumerate those having small size. For some classes of indecomposable involutive solutions recently studied in the literature, we compute the exact value of the primitive level. Some relationships with other families of solutions are also discussed. Finally, following [13, Question 3. 2], we provide a complete description of those having primitive level 2 by left braces.
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Language:	Anglès
Document:	Article ; recerca ; Versió publicada
Subject:	Imprimitive group ; Yang-Baxter equation ; Brace ; Cycle set
Published in:	Publicacions matemàtiques, Vol. 69 Núm. 2 (2025) , p. 429-444 (Articles) , ISSN 2014-4350

Adreça original: https://raco.cat/index.php/PublicacionsMatematiques/article/view/10000006177
DOI: 10.5565/PUBLMAT6922509

16 p, 341.4 KB

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