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math.GR2025
On some semidirect products of skew braces arising in Hopf-Galois theory
Paul J. Truman
We classify skew braces that are the semidirect product of an ideal and a left ideal. As a consequence, given a Galois extension of fields whose Galois group is the semidir…
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…