Related papers: Galois correspondence for group-type partial actio…

We prove the Galois correspondence between the subgroups of a finite automorphism group G of a simple vertex operator algebra V and the vertex operator subalgebras of V containing the set V^G of G-invariants.

We present some generalizations of the well-known correspondence, found by R. Exel, between partial actions of a group $G$ on a set $X$ and semigroup homomorphism of $S(G)$ on the semigroup $I(X)$ of partial bijections of $X,$ being $S(G)$…

For an arbitrary localic etale groupoid G we provide simple descriptions, in terms of modules over the quantale O(G) of the groupoid, of the continuous actions of G, including actions on open maps and sheaves. The category of G-actions is…

In this paper, we are interested in the study of the existence of connections between partial groupoid actions and partial group actions. Precisely, we prove that there exists a datum connecting a partial action of a connected groupoid and…

Consider a finite group $G$ acting on a Riemann surface $S$, and the associated branched Galois cover $\pi_G:S \to Y=S/G$. We introduce the concept of geometric signature for the action of $G$, and we show that it captures the information…

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…

We prove that the Galois groupoid of the category of $G$-spectra for a finite group $G$ is algebraic, i.e. equivalent to the \'etale fundamental groupoid of the Burnside ring of $G$. We implement an algorithm that computes the latter from…

Given a group G, we construct, in a canonical way, an inverse semigroup S(G) associated to G. The actions of S(G) are shown to be in one-to-one correspondence with the partial actions of G, both in the case of actions on a set, and that of…

We establish rigidity for partial transformation groupoids associated with algebraic actions of semigroups: If two such groupoids (satisfying appropriate conditions) are isomorphic, then the globalizations of the initial algebraic actions…

Let $n$ be a positive integer and $R=(M_{ij})_{1\leq i,j\leq n}$ be a generalized matrix ring. For each $1\leq i,j\leq n$, let $I_i$ be an ideal of the ring $R_i:=M_{ii}$ and denote $I_{ij}=I_iM_{ij}+M_{ij}I_j$. We give sufficient…

We study the relations between partial and global group cohomology with values in a commutative unital ring $\mathcal{A}$. In particular, for a unital partial action of a group $G$ on $\mathcal{A}$, such that $\mathcal{A}$ is a direct…

Some conditions for the Galois map to be injective are given in the groupoid acting on a noncommutative ring context. In the particular case in which the Galois extension is a central Galois algebra, it is given a complete characterization…

We prove a structure result on proper extensions of two-sided restriction semigroups in terms of partial actions, generalizing respective results for monoids and for inverse semigroups and upgrading the latter. We introduce and study…

If $\mathfrak{g} \subseteq \mathfrak{h}$ is an extension of Lie algebras over a field $k$ such that ${\rm dim}_k (\mathfrak{g}) = n$ and ${\rm dim}_k (\mathfrak{h}) = n + m$, then the Galois group ${\rm Gal} \, (\mathfrak{h}/\mathfrak{g})$…

The aim of this paper is to characterize the notion of internal category (groupoid) in the category of Leibniz algebras and investigate the properties of well-known notions such as covering groupoid and groupoid operations (actions) in this…

Given a partial action $\alpha$ of a connected groupoid $\mathcal{G}$ on an associative ring $A$ we investigate under what conditions the partial skew groupoid ring $A\star_{\alpha}\mathcal{G}$ can be realized as a partial skew group ring.…

In this article we construct the inverse semigroup of equivalence classes of partial Galois abelian extensions of a commutative ring R with same group G, called the Harrison partial inverse semigroup.

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…

In this paper we present Cohen-Montgomery-type duality theorems for groupoid (co)actions.

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