论文标题
逆半群的一致性引起的通用典型类固醇的不变集和正常的亚组
Invariant sets and normal subgroupoids of universal étale groupoids induced by congruences of inverse semigroups
论文作者
论文摘要
对于给定的逆半群，可以将称为通用群体的典型群体固定相关联。我们的动机是研究逆半群和相关的of oltale gropsoid之间的关系。在本文中，我们专注于反向半群的一致性，这是考虑反向半群的商的基本概念。我们证明，逆半群的一致性会诱导封闭的不变集和普通类固醇的正常亚组。然后，我们表明，与商逆半群相关的通用群体由原始通用群体的限制和商描述。最后，我们计算包括阿贝利亚化在内的特殊一致性引起的不变集和正常的亚组。
For a given inverse semigroup, one can associate an étale groupoid which is called the universal groupoid. Our motivation is studying the relation between inverse semigroups and associated étale groupoids. In this paper, we focus on congruences of inverse semigroups, which is a fundamental concept to consider quotients of inverse semigroup. We prove that a congruence of an inverse semigroup induces a closed invariant set and a normal subgroupoid of the universal groupoid. Then we show that the universal groupoid associated to a quotient inverse semigroup is described by the restriction and quotient of the original universal groupoid. Finally we compute invariant sets and normal subgroupoids induced by special congruences including abelianization.
