Constructing skew bracoids via abelian maps, and solutions to the Yang-Baxter equation

Koch, Alan; Truman, Paul J.

Abstract

We show how one can use the skew braces constructed using abelian maps to generate families of skew bracoids as defined by Martin-Lyons and Truman. Under certain circumstances, these bracoids give right non-degenerate solutions to the Yang-Baxter equation.

Citation

Koch, A., & Truman, P. J. (2025). Constructing skew bracoids via abelian maps, and solutions to the Yang-Baxter equation. Journal of Algebra, 684, 336-353. https://doi.org/10.1016/j.jalgebra.2025.07.013

• Journal Article Type: Article
• Acceptance Date: Jul 16, 2025
• Online Publication Date: Jul 22, 2025
• Publication Date: Dec 15, 2025
• Deposit Date: Aug 13, 2025
• Publicly Available Date: Aug 14, 2025
• Journal: Journal of Algebra
• Print ISSN: 0021-8693
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 684
• Pages: 336-353
• DOI: https://doi.org/10.1016/j.jalgebra.2025.07.013
• Public URL: https://keele-repository.worktribe.com/output/1366098
• Publisher URL: https://www.sciencedirect.com/science/article/pii/S0021869325004223?via%3Dihub
• Additional Information: This article is maintained by: Elsevier; Article Title: Constructing skew bracoids via abelian maps, and solutions to the Yang-Baxter equation; Journal Title: Journal of Algebra; CrossRef DOI link to publisher maintained version: https://doi.org/10.1016/j.jalgebra.2025.07.013; Content Type: article; Copyright: © 2025 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.