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arXiv · 1905.05886

Factorizations of skew braces

E. Jespers·Ł. Kubat·A. Van Antwerpen·L. Vendramin
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Abstract

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 It\^{o}'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 ideals.

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E. Jespers, Ł. Kubat, A. Van Antwerpen, L. Vendramin. 2019-05-14. Factorizations of skew braces. https://doi.org/10.1007/s00208-019-01909-1

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