Artículo
Skew braces and the Yang-Baxter equation
Fecha de publicación:
09/2017
Editorial:
American Mathematical Society
Revista:
Mathematics Of Computation
ISSN:
0025-5718
Idioma:
Inglés
Tipo de recurso:
Artículo publicado
Clasificación temática:
Resumen
Braces were introduced by Rump to study non-degenerate involutive set-theoretic solutions of the Yang-Baxter equation. We generalize Rump's braces to the non-commutative setting and use this new structure to study not necessarily involutive non-degenerate set-theoretical solutions of the Yang-Baxter equation. Based on results of Bachiller and Catino and Rizzo, we develop an algorithm to enumerate and construct classical and non-classical braces of small size up to isomorphism. This algorithm is used to produce a database of braces of small size. The paper contains several open problems, questions and conjectures.
Palabras clave:
Brace
,
Yang-Baxter
,
1-Cocycle
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Articulos(IMAS)
Articulos de INSTITUTO DE INVESTIGACIONES MATEMATICAS "LUIS A. SANTALO"
Articulos de INSTITUTO DE INVESTIGACIONES MATEMATICAS "LUIS A. SANTALO"
Citación
Guarnieri, Leandro; Vendramin, Claudio Leandro; Skew braces and the Yang-Baxter equation; American Mathematical Society; Mathematics Of Computation; 86; 307; 9-2017; 2519-2534
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