论文标题
偏向左括号和同构问题，用于Galois扩展的Hopf-Galois结构
Skew left braces and isomorphism problems for Hopf-Galois structures on Galois extensions
论文作者
论文摘要
考虑到有限的$ g $，我们研究了$ g $的一组定期子组，这些定期子组发生在两种类型的代数对象的分类理论中：偏向左括号，具有多态同构至$ g $ to $ g $和hopf-galois结构，而hopf-galois结构则由galois Galois Group Group Group Group usomerphics $ GOMORPHIC $ GOMORPHIC $ GOMORPHIC $ GOMORPHIC $ GOMORPHIC $ GOMORPHIC $ GOMORPHIC，我们研究了两个这样的亚组何时产生涉及同构HOPF代数的同构偏斜的左括号或Hopf-Galois结构的问题。特别是，我们表明，在某些情况下，Hopf代数的同构类别给出了Hopf-Galois结构，由相应的偏斜左支架确定。我们在文献中各种现有结构的背景下研究了这些问题。作为我们的结果的应用，我们将同态截然不同的HOPF代数分类为$ p> q $ prime数字的GALOIS扩展为$ PQ $的GALOIS结构。
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 Hopf-Galois structures admitted by a Galois extension of fields with Galois group isomorphic to $ G $. We study the questions of when two such subgroups yield isomorphic skew left braces or Hopf-Galois structures involving isomorphic Hopf algebras. In particular, we show that in some cases the isomorphism class of the Hopf algebra giving a Hopf-Galois structure is determined by the corresponding skew left brace. We investigate these questions in the context of a variety of existing constructions in the literature. As an application of our results we classify the isomorphically distinct Hopf algebras that give Hopf-Galois structures on a Galois extension of degree $ pq $ for $ p>q $ prime numbers.
