2024/04/24 by Ilaria Colazzo, Alan Koch, Colazzo, Ilaria +5
Mathematics · #Advanced Topics in Algebra #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology #Primary 16T25 #Rings and Algebras (math.RA) #Secondary 20N99
paper · pdf · doi:10.48550/arxiv.2404.15929
openalex publication_date 2024/04/24 · openalex created_date 2024/04/27 · openalex updated_date 2026/07/28
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.