Factorizations of skew braces
By Eric Jespers, Ł. Kubat, A. V. Antwerpen, Leandro Vendramin. Mathematische Annalen, 2019
47 citations recorded by the source corpus.
We introduce strong left ideals of skew braces and prove that they produce non-trivial decomposition of set-theoretic solutions of the Yang–Baxter equation. We study factorization of skew left braces through strong left ideals and we prove analogs of Itô’s theorem in the context of skew left braces. As a corollary, we obtain applications to the retractability problem of involutive non-degenerate solutions of the Yang–Baxter equation. Finally, we classify skew braces that contain no non-trivial proper characteristic ideals.
Subfields: Algebra and Number Theory, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/f3c1ecfa77aa75cc6b8a11344366c157d34fa822
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In Algebra and Number Theory
In Geometry and Topology
Citations in the corpus
- Post-groups, (Lie-)Butcher groups and the Yang–Baxter equation (2023, unknown): “The nilpotency and factorization of skew-left braces were investigated in [10, 33].”
- Rota—Baxter groups, skew left braces, and the Yang—Baxter equation (2021, methodology): “Strong left ideals provide decompositions of the corresponding solutions to the Yang—Baxter equation [26] and they are connected with intermediate fields of a Galois field extension [31].”