Zobrazeno 1 - 10
of 123
pro vyhledávání: '"Koch, Alan"'
Skew braces provide an algebraic framework for studying bijective nondegenerate solutions of the set-theoretic Yang-Baxter equation. We show that left skew bracoids, recently introduced by two of the authors, can be used to obtain right nondegenerate
Externí odkaz:
http://arxiv.org/abs/2404.15929
Autor:
Koch, Alan
Let $G$ be a nonabelian group. We show how a collection of compatible endomorphisms $\psi_i:G\to G$ such that $\psi_i([G,G])\le Z(G)$ for all $i$ allows us to construct a family of bi-skew braces called a brace block. We relate this construction to o
Externí odkaz:
http://arxiv.org/abs/2206.07540
Autor:
Koch, Alan
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 $\{\circ_n: n\in \mathbb Z^{\ge 0}\}$ on $G$ such that $(G,\circ_m,\circ_n)$ is a skew left brace for all $m,n\ge
Externí odkaz:
http://arxiv.org/abs/2102.06104
Autor:
Koch, Alan
Let $G$ be a finite nonabelian group, and let $\psi:G\to G$ be a homomorphism with abelian image. We show how $\psi$ gives rise to two Hopf-Galois structures on a Galois extension $L/K$ with Galois group (isomorphic to) $G$; one of these structures g
Externí odkaz:
http://arxiv.org/abs/2007.08967
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 endomorphism gives rise to two non-degenerate solutions to the Yang-B
Externí odkaz:
http://arxiv.org/abs/2006.13196
Autor:
Koch, Alan, Truman, Paul J.
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: skew left braces with multiplicative group isomorphic to $ G $ and Hop
Externí odkaz:
http://arxiv.org/abs/2005.05809
Autor:
Koch, Alan, Truman, Paul J.
Given a skew left brace $\mathfrak{B}$, we introduce the notion of an "opposite" skew left brace $\mathfrak{B}'$, which is closely related to the concept of the opposite of a group, and provide several applications. Skew left braces are closely linke
Externí odkaz:
http://arxiv.org/abs/1908.02682
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 giving a Hopf-Galois structure on $ L/K $ has the form $ E[N]^{G} $ for som
Externí odkaz:
http://arxiv.org/abs/1711.05554
We discuss isomorphism questions concerning the Hopf algebras that yield Hopf-Galois structures for a fixed separable field extension $L/K$. We study in detail the case where $L/K$ is Galois with dihedral group $D_p$, $p\ge 3$ prime and give explicit
Externí odkaz:
http://arxiv.org/abs/1708.09822