3 papers
math.GR2026
Bidihedral skew braces
Alan Koch, Paul J. Truman
We classify skew braces with additive and multiplicative groups both isomorphic to the dihedral group . As a consequence, we obtain an alternative proof of the classificat…
math.RA2025
Skew bracoids containing a skew brace
Ilaria Colazzo, Alan Koch, Isabel Martin-Lyons +1
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…
math.GR2025
Constructing skew bracoids via abelian maps, and solutions to the {Y}ang-{B}axter equation
Alan Koch, Paul J. Truman
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, the…