Related papers: Partial actions on quotient spaces and globalizati…

We prove that every ordered partial action of an inverse semigroupoid on a partially ordered set admits a globalization. This result is used to establish a connection between ordered partial actions of groupoids and a multi-object analogue…

We develop a cohomology theory of groups based on partial actions and explore its relation with the partial Schur multiplier as well as with cohomology of inverse semigroups.

We first introduce an invariant index for G-equivariant elliptic differential operators on a locally compact manifold M admitting a proper cocompact action of a locally compact group G. It generalizes the Kawasaki index for orbifolds to the…

The effectiveness of the aplication of constructions in $G$-graded $k$-categories to the computation of the fundamental group of a finite dimensional $k$-algebra, alongside with open problems still left untouched by those methods and new…

We extend the classicial notion of an outer action $\alpha$ of a group $G$ on a unital ring $A$ to the case when $\alpha$ is a partial action on ideals, all of which have local units. We show that if $\alpha$ is an outer partial action of…

We study topological properties of semi-group actions on the circle by orientation-preserving homeomorhisms. We prove that a generic action either possesses a forward-invariant interval-domain (i.e. a finite union of disjoint circle arcs),…

We study polar actions with horizontal sections on the total space of certain principal bundles $G/K\to G/H$ with base a symmetric space of compact type. We classify such actions up to orbit equivalence in many cases. In particular, we…

Let X be a G-space such that the orbit space X/G is metrizable. Suppose a family of slices is given at each point of X. We study a construction which associates, under some conditions on the family of slices, with any metric on X/G an…

Let $A$ be an additively cancellative semialgebra over an additively cancellative semifield $K$ as defined in [9]. For a given partial action $\alpha$ of a group $G$ on an algebra, the associativity of partial skew group ring together with…

In this paper, we introduce the notion of globalization for partial module coalgebra and for partial comodule coalgebra. We show that every partial module coalgebra is globalizable exhibiting a standard globalization. We also show the…

For actions with a dense orbit of a connected noncompact simple Lie group $G$, we obtain some global rigidity results when the actions preserve certain geometric structures. In particular, we prove that for a $G$-action to be equivalent to…

Let $X$ be an algebraic variety over $\mathbb{C}$ and $G$ be an algebraic group acting on $X$ whose action is closed. J. Poineau defined a compactification $X^\urcorner$ of $X(\mathbb{C})$ by using hybrid Berkovich spaces. We will focus on…

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 article, we introduce the concept of partial actions of a group $G$ on quivers and demonstrate that for any given partial action of G on a quiver $\Gamma$, there exists another quiver, $\Gamma'$ with a full $G$-action. This is an…

We establish lower bounds on the dimensions in which arithmetic groups with torsion can act on acyclic manifolds and homology spheres. The bounds rely on the existence of elementary p-groups in the groups concerned. In some cases, including…

We introduce "geometric" partial comodules over coalgebras in monoidal categories, as an alternative notion to the notion of partial action and coaction of a Hopf algebra introduced by Caenepeel and Janssen. The name is motivated by the…

Given an inverse semigroup $S$ endowed with a partial action on a topological space $X$, we construct a groupoid of germs $S\ltimes X$ in a manner similar to Exel's groupoid of germs, and similarly a partial action of $S$ on an algebra $A$…

We characterize supramenable groups in terms of existence of invariant probability measures for partial actions on compact Hausdorff spaces and existence of tracial states on partial crossed products. These characterizations show that, in…

The first part of this paper is a refinement of Winkelmann's work on invariant rings and quotients of algebraic groups actions on affine varieties, where we take a more geometric point of view. We show that the (algebraic) quotient…

We provide an explicit construction of quasi-invariant measures on polarized coadjoint orbits of a Lie group G. The use of specific (trivial) central extensions of G by the multiplicative group ${R}^+$ allows us to restore the strict…