Related papers: Galois Correspondence for Partial Groupoid Actions

It is well known that the Galois group of an extension puts constraints on the structure of the relative ideal class groups. Using only basic parts of the theory of group representations, we give a unified approach to such results.

We consider the category of partial actions, where the group and the set upon which the group acts can vary. Within this framework, we develop a theory of quotient partial actions and prove that this category is both (co)complete and…

Proposing a certain category of bialgebroid maps we show that the balanced depth 2 extensions appear as they were the finitary Galois extensions in the context of quantum groupoid actions, i.e., actions by finite bialgebroids, weak…

For a partial Galois extension of commutative rings we give a seven terms sequence, which is an analogue of the Chase-Harrison-Rosenberg sequence.

A global action is an algebraic analogue of a topological space. It consists of group actions $G_\alpha\curvearrowright X_\alpha$, $(\alpha\in\Phi)$, which fulfill a certain compatibility condition. We investigate the homotopy theory of…

This paper is a new contribution to the partial Galois theory of groups. First, given a unital partial action $\alpha_G$ of a finite group $G$ on an algebra $S$ such that $S$ is an $\alpha_G$-partial Galois extension of $S^{\alpha_G}$ and a…

For a given inverse semigroup action on a topological space, one can associate an \'etale groupoid. We prove that there exists a correspondence between the certain subsemigroups and the open wide subgroupoids in case that the action is…

In this article, we introduce the concept of partial groupoid actions on R- semicategories as well as we give criteria for existence of a globalization of it. This point of view is a generalization of the notions of partial groupoid actions…

The main goal of this paper is to introduce the notion of twisted partial action of groupoids. We generalize the theorem about the existence of an enveloping action, also known as the globalization theorem, and show that the crossed…

Using an algebraic point of view we present an introduction to the groupoid theory, that is, we give fundamental properties of groupoids as, uniqueness of inverses and properties of the identities, and study subgroupoids, wide subgroupoids…

In the first part of this paper we try to explain to a general mathematical audience some of the remarkable web of conjectures linking representations of Galois groups with algebraic geometry, complex analysis and discrete subgroups of Lie…

In a previous work, the second-named author gave a complete description of the action of automorphisms on the ordinary irreducible characters of the finite symplectic groups. We generalise this in two directions. Firstly, using work of the…

Let $\alpha=(A_g,\alpha_g)_{g\in G}$ be a group-type partial action of a connected groupoid $G$ on a ring $A=\bigoplus_{z\in G_0}A_z$ and $B=A\star_{\alpha}G$ the corresponding partial skew groupoid ring. In the first part of this paper we…

Some basic notions and results in Topological Dynamics are extended to continuous groupoid actions in topological spaces. We focus mainly on recurrence properties. Besides results that are analogous to the classical case of group actions,…

We establish the faithfulness of a geometric action of the absolute Galois group of the rationals that can be defined on the discriminantal variety associated to a finite complex reflection group, and review some possible connections with…

We make explicit certain results around the Galois correspondence in the context of definable automorphism groups, and point out the relation to some recent papers dealing with the Galois theory of algebraic differential equations when the…

In this paper, we generalize the definition of the differential Galois group and the Galois correspondence theorem established previously for Picard-Vessiot extensions of real differential fields with real closed field of constants to any…

We provide a necessary and sufficient condition to the existence of an ordered globalization of a partial ordered action of an ordered groupoid on a ring and we also present criteria to obtain uniqueness. Furthermore, we apply those results…

Groupoid actions on C*-bundles and inverse semigroup actions on C*-algebras are closely related when the groupoid is r-discrete.

We introduce and develop a structure theory of a new class of noncommutative rings - Galois orders, that generalize classical orders in noncommutative rings. Galois orders realized as certain subrings of invariants in skew semigroup rings.…