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

We prove a Galois correspondence theorem for groupoids acting orthogonally and partially on commutative rings. We also consider partial actions that are not orthogonal, presenting two correspondences in this case: one for strongly Galois…

A Galois correspondence theorem is proved for the case of inverse semigroups acting orthogonally on commutative rings as a consequence of the Galois correspondence theorem for groupoid actions. To this end, we use a classic result of…

In this paper we present a Galois-Grothendieck-type correspondence for groupoid actions. As an application a Galois-type correspondence is also given.

In this paper, we prove a Galois correspondence for compact group actions on C*-algebras in the presence of a commuting minimal action. Namely, we show that there is a one to one correspondence between the C*-subalgebras that are globally…

We develop a Galois theory of commutative rings under actions of finite inverse semigroups. We present equivalences for the definition of Galois extension as well as a Galois correspondence theorem. We also show how the theory behaves in…

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…

We establish a Galois correspondence for finite quantum groupoid actions on II_1 factors and show that every finite index and finite depth subfactor is an intermediate subalgebra of a quantum groupoid crossed product. Moreover, any such a…

We establish a Galois correspondence for a minimal action of a compact quantum group ${\mathbb G}$ on a von Neumann factor $M$. This extends the result of Izumi, Longo and Popa who treated the case of a Kac algebra. Namely, there exists a…

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…

In this paper we introduce the notion of a partial action of a groupoid on a ring as well as we give a criteria for the existence of a globalization of it. We construct a Morita context associated to a globalizable partial groupoid action…

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…

We show that there is a one-to-one correspondence between the partial actions of a groupoid $G$ on a set $X$ and the inverse semigroupoid actions of the Exel's inverse semigroupoid $S(G)$ on $X$. We also define inverse semigroupoid…

This unpublished note contains some materials taken from my old study note on groupoids and small categories. It contains a proof for the fact that any groupoid is a group bundle over an equivalence relation. Moreover, the action of a…

Given a partial action $\alpha=(A_g,\alpha_g)_{g\in \mathcal{G}}$ of a connected groupoid $\mathcal{G}$ on a ring $A$ and an object $x$ of $\mathcal{G}$, the isotropy group $\mathcal{G}(x)$ acts partially on the ideal $A_x$ of $A$ by the…

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…

A geometric interpretation and generalisation for the Galois action on finite group character tables is sketched. The generalisation is a Galois action on the space Map_G(G^n,\bar{Q})/S_n for each finite G, where G acts by simultaneous…

Let a discrete group $G$ act on a unital simple C$^*$-algebra $A$ by outer automorphisms. We establish a Galois correspondence $H\mapsto A\rtimes_{\alpha,r}H$ between subgroups of $G$ and C$^*$-algebras $B$ satisfying $A\subseteq B…

Given a partial (resp. a global) action $\alpha$ of a connected finite groupoid $G$ on a ring $A$, we determine necessary and sufficient conditions for the partial (resp. global) skew groupoid ring $A\star_{\alpha} G$ to be a separable…

In this paper, we study partial actions of groups on $R$-algebras, where $R$ is a commutative ring. We describe the partial actions of groups on the indecomposable algebras with enveloping actions. Then we work on algebras that can be…

For a semifield extension $T /S$, an action of a finite group $G$ on $T$ is Galois if $(1)$ the $G$-invariant subsemifield of $T$ is $S$ and $(2)$ subgroups of $G$ whose invariant semifields coincide are equal. We show that for a finite…