Paul J. Truman

activity

20172020

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

1 citations · 1 across the 2 of their papers we have counts for

collaborators

6 papers

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…

math.NT2019

Hopf-Galois module structure of tamely ramified radical extensions of prime degree

Paul J Truman

Let $K$ be a number field and let $L / K$ be a tamely ramified radical extension of prime degree $p$ . If $K$ contains a primitive $p^{t h}$ root of unity then $L / K$ is a c…

math.RA2018

The structure of Hopf algebras giving Hopf-Galois structures on Quaternionic extensions

Stuart Taylor, Paul J Truman

Let $L / F$ be a Galois extension of fields with Galois group isomorphic to the quaternion group of order $8$ . We describe all of the Hopf-Galois structures admitted by $L / F$ , an…

math.NT2017

Isomorphism problems for Hopf-Galois structures on separable field extensions

Alan Koch, Timothy Kohl, Paul J. Truman +1

Let $L / K$ be a finite separable extension of fields whose Galois closure $E / K$ has group $G$ . Greither and Pareigis have used Galois descent to show that a Hopf algebra givin…

math.NT2017

Normality and Short Exact Sequences of Hopf-Galois Structures

Alan Koch, Timothy Kohl, Paul J. Truman +1

Every Hopf-Galois structure on a finite Galois extension $K / k$ where $G = G a l (K / k)$ corresponds uniquely to a regular subgroup $N \leq B = Perm (G)$ , normalized by $λ(G)\l…