Alan Koch

activity

20172021

most citedAbelian fixed point free endomorphisms and the Yang-Baxter equation

1 citations · 1 across the 3 of their papers we have counts for

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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.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…