论文标题
群体及其类固醇环的非亚伯扩展
Non-Abelian extensions of groupoids and their groupoid rings
论文作者
论文摘要
我们提出了一种几何定向的分类理论，用于对韦斯特曼（Westman）的亚伯分类理论的非阿布尔分类理论，以及韦斯特曼（Westman）的阿贝尔（Abelian）扩展理论，以及熟悉的分类理论，用于Schreier和Eilenberg-Maclane的非阿布尔分类理论。作为我们技术的应用，我们证明了groupoids $ \ nathcal {n} \ to \ nathcal {e} \ to \ nathcal {g} $的每个延伸产生$ \ natercal {g} $的群体串联产品，由$ \ nathcal n $ up up up proups $ up proups $ up prouns $ up concouncon up up proups，同构。此外，我们对我们的分类方法自然地转移到了群体交叉产品的类别中，从而为这类环提供了分类理论。我们的研究是由搜索群体交叉产品的自然实例的动机。
We present a geometrically oriented classification theory for non-Abelian extensions of groupoids generalizing the classification theory for Abelian extensions of groupoids by Westman as well as the familiar classification theory for non-Abelian extensions of groups by Schreier and Eilenberg-MacLane. As an application of our techniques we demonstrate that each extension of groupoids $\mathcal{N} \to \mathcal{E} \to \mathcal{G}$ gives rise to a groupoid crossed product of $\mathcal{G}$ by the groupoid ring of $\mathcal{N}$ which recovers the groupoid ring of $\mathcal{E}$ up to isomorphism. Furthermore, we make the somewhat surprising observation that our classification methods naturally transfer to the class of groupoid crossed products, thus providing a classification theory for this class of rings. Our study is motivated by the search for natural examples of groupoid crossed products.
