Solutions of the Yang-Baxter equation associated with a left brace

By D. Bachiller, Ferran Cedó, Eric Jespers. 2015

79 citations recorded by the source corpus.

Given a left brace $G$, a method to construct all the involutive, non-degenerate set-theoretic solutions $(Y,s)$ of the YBE, such that $\mathcal{G}(Y,s)\cong G$ is given. This method depends entirely on the brace structure of $G$.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/7877cd956c28451228f2bd9d39218ebfa64c2781

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In Algebra and Number Theory

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Extensions, matched products, and simple braces (2015, result): “But moreover, using the recent results of [3], given a left brace B, we can recover from B all the solutions (X, r) such that G(X, r) ∼= B as left braces.”
On Engel groups, nilpotent groups, rings, braces and the Yang-Baxter equation (2015, background): “There are many interesting results in this area [10, 11, 12, 13, 18, 20, 19, 22, 27, 44, 29, 55].”
Solutions of the Yang–Baxter equation associated to skew left braces, with applications to racks (2016, methodology): “erate solutions with additional properties, like square-free (Section 3.4), involutive (Section 4.5), or irretractable (Section 4.8) solutions. The result about the involutive case is originally from [5], but here we show how it ﬁts in the general setting. As an example of all these techniques, we s”
Iterated matched products of finite braces and simplicity; new solutions of the Yang-Baxter equation (2016, methodology): “Given a left brace B, in [4] a method is given to construct explicitly all the solutions (X, r) of the YBE such that G(X, r) ∼= B as left braces.”