论文标题
{h} opf- {g} alois结构
Abelian maps, bi-skew braces, and opposite pairs of {H}opf-{G}alois structures
论文作者
论文摘要
令$ g $为有限的非阿布尔群体，让$ψ：g \ t to g $是带有Abelian Image的同态。我们展示了$ψ$如何与Galois Group（同构为$ G $）一起在Galois扩展名$ L/K $上产生两个Hopf-Galois结构；这些结构之一概括了Childs在2013年引入的``固定点的固定点'Abelian内态''所给出的结构。我们构建了与上面两个Hopf-Galois结构相对应的偏斜左支架。我们将证明，左括号之一实际上是双态支架，使我们能够为Yang-baxter方程以及一对（潜在的）不同有限galois扩展的一对hopf-galois结构获得四种固定的理论解决方案。
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 $L/K$ with Galois group (isomorphic to) $G$; one of these structures generalizes the construction given by a ``fixed point free abelian endomorphism'' introduced by Childs in 2013. We construct the skew left brace corresponding to each of the two Hopf-Galois structures above. We will show that one of the skew left braces is in fact a bi-skew brace, allowing us to obtain four set-theoretic solutions to the Yang-Baxter equation as well as a pair of Hopf-Galois structures on a (potentially) different finite Galois extension.
