Factorizations of skew braces
Rings and Algebras
2019-10-30 v1 Group Theory
Quantum Algebra
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.
Keywords
Cite
@article{arxiv.1905.05886,
title = {Factorizations of skew braces},
author = {E. Jespers and Ł. Kubat and A. Van Antwerpen and L. Vendramin},
journal= {arXiv preprint arXiv:1905.05886},
year = {2019}
}
Comments
12 pages