Abstract:
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. © 2017 American Mathematical Society.
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Citas:
---------- APA ----------
Guarnieri, L. & Vendramin, L.
(2017)
. Skew braces and the Yang-Baxter equation. Mathematics of Computation, 86(307), 2519-2534.
http://dx.doi.org/10.1090/mcom/3161---------- CHICAGO ----------
Guarnieri, L., Vendramin, L.
"Skew braces and the Yang-Baxter equation"
. Mathematics of Computation 86, no. 307
(2017) : 2519-2534.
http://dx.doi.org/10.1090/mcom/3161---------- MLA ----------
Guarnieri, L., Vendramin, L.
"Skew braces and the Yang-Baxter equation"
. Mathematics of Computation, vol. 86, no. 307, 2017, pp. 2519-2534.
http://dx.doi.org/10.1090/mcom/3161---------- VANCOUVER ----------
Guarnieri, L., Vendramin, L. Skew braces and the Yang-Baxter equation. Math. Comput. 2017;86(307):2519-2534.
http://dx.doi.org/10.1090/mcom/3161