Alan Koch

activity

20102022

most citedScaffolds and integral Hopf Galois module structure on purely inseparable extensions

5 citations · 14 across the 9 of their papers we have counts for

collaborators

13 papers

math.GR2022

Commutator-central maps, brace blocks, and {H}opf-{G}alois structures on {G}alois extensions

Alan Koch

Let $G$ be a nonabelian group. We show how a collection of compatible endomorphisms $ψ_{i} : G \to G$ such that $ψ_{i} ([G, G]) \leq Z (G)$ for all $i$ allows us to construct a family of bi-sk…

math.GR2021

Abelian maps, brace blocks, and solutions to the {Y}ang-{B}axter equation

Alan Koch

Let $G$ be a finite nonabelian group. We show how an endomorphism of $G$ with abelian image gives rise to a family of binary operations ${\circ_{n} : n \in Z^{\geq 0}}$ on $G$ …

math.GR2020

Abelian maps, bi-skew braces, and opposite pairs of {H}opf-{G}alois structures

Alan Koch

Let $G$ be a finite nonabelian group, and let $ψ : G \to G$ be a homomorphism with abelian image. We show how $ψ$ gives rise to two Hopf-Galois structures on a Galois extension $L / K$ …

math.GR2020★ 1 cited

Abelian fixed point free endomorphisms and the Yang-Baxter equation

Alan Koch, Laura Stordy, Paul J. Truman

We obtain a simple family of solutions to the set-theoretic Yang-Baxter equation, one which depends only on considering special endomorphisms of a finite group. We show how such an…

math.GR2020

Skew left braces and isomorphism problems for Hopf-Galois structures on Galois extensions

Alan Koch, Paul J. Truman

Given a finite group $G$ , we study certain regular subgroups of the group of permutations of $G$ , which occur in the classification theories of two types of algebraic objects:…

math.GR2019

Opposite skew left braces and applications

Alan Koch, Paul J. Truman

Given a skew left brace $B$ , we introduce the notion of an "opposite" skew left brace $B^{'}$ , which is closely related to the concept of the opposite of a group…