Skew bracoids containing a skew brace

Colazzo, Ilaria; Koch, Alan; Martin-Lyons, Isabel; Truman, Paul J.

Abstract

Skew bracoids have been shown to have applications in Hopf-Galois theory. We show that a certain family of skew bracoids correspond bijectively with left cancellative semibraces. A consequence of this correspondence is that skew bracoids in this family can be used to obtain and study solutions of the set-theoretic Yang-Baxter equation; we study this process and the resulting solutions. We give numerous examples of skew bracoids satisfying our hypothesis, drawing upon a variety of constructions in the literature.

Citation

Colazzo, I., Koch, A., Martin-Lyons, I., & Truman, P. J. (2025). Skew bracoids containing a skew brace. Journal of Algebra and Its Applications, https://doi.org/10.1142/S021949882650235X

• Journal Article Type: Article
• Acceptance Date: Apr 8, 2025
• Online Publication Date: Apr 17, 2025
• Publication Date: Apr 17, 2025
• Deposit Date: Apr 29, 2025
• Publicly Available Date: Apr 29, 2025
• Journal: Journal of Algebra and Its Applications
• Print ISSN: 0219-4988
• Electronic ISSN: 1793-6829
• Peer Reviewed: Peer Reviewed
• DOI: https://doi.org/10.1142/S021949882650235X
• Public URL: https://keele-repository.worktribe.com/output/1202452
• Publisher URL: https://doi.org/10.1142/S021949882650235X