Work

Skew bracoids containing a skew brace

Year: 2025

Type: article

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.

Source: Journal of Algebra and Its Applications

DOI: 10.1142/s021949882650235x

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

Institutions: University of Exeter, Agnes Scott College, Keele University

Language: English

Topic: Advanced Topics in Algebra

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: London Mathematical Society, Engineering and Physical Sciences Research Council

Awards: Hopf-Galois Theory and Skew Braces, Weak skew left braces, Hopf-Galois theory, and the Yang-Baxter equation