Related papers: Globalizations for partial (co)actions on coalgebr…
We study the globalization of partial actions on sets and topological spaces and of partial coactions on algebras by applying the general theory of globalization for geometric partial comodules, as previously developed by the authors. We…
Partial actions of Hopf algebras can be considered as a generalization of partial actions of groups on algebras. Among important properties of partial Hopf actions, it is possible to prove the existence of enveloping actions, i.e., every…
The aim of this paper is to prove the statement in the title. As a by-product, we obtain new globalization results in cases never considered before, such as partial corepresentations of Hopf algebras. Moreover, we show that for partial…
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…
In this work the notions of partial action of a weak Hopf algebra on a coalgebra and partial action of a groupoid on a coalgebra will be introduced, just as some important properties. An equivalence between these notions will be presented.…
In this paper we introduce the notions of partial bimodule algebra and partial bico- module algebra. We also deal with the existence of globalizations for these structures, generalizing related results appeared in [2, 4]. As an application…
We study the problem of constructing a globalization for partial actions on *-algebras, C*-algebras and Hilbert modules. For the first ones we give a necessary condition for the existence of a globalization and we prove this conditions is…
Given a partial action $\theta$ of a group on a set with an algebraic structure, we construct a reflector of $\theta$ in the corresponding subcategory of global actions and study the question when this reflector is a globalization. In…
In this work, we review some properties of twisted partial actions of Hopf algebras on unital algebras and give necessary and sufficient conditions for a twisted partial action to have a globalization. We also elaborate a series of…
We discuss globalization for geometric partial comodules in a monoidal category with pushouts and we provide a concrete procedure to construct it, whenever it exists. The mild assumptions required by our approach make it possible to apply…
We extend the concept of a partial group action to non-associative algebras in a variety \(\mathcal{V}(I)\), solve the globalization problem within \(\mathcal{V}(I)\) and examine its universal property. It is achieved using what we call the…
In partial action theory, a pertinent question is whenever given a partial (co)action of a Hopf algebra A on an algebra R, it is possible to construct an enveloping (co)action. The authors Alves and Batista, in [2],have shown that this is…
We prove that every partial action of an inverse semigroupoid on a set admits a universal globalization. Moreover, we show that our construction gives a reflector from the category of partial actions on the full subcategory of global…
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…
We study the globalization problem for a strong partial action $\alpha$ of a monoid $M$ on a semigroup $X$ via the associated rewriting system $(X_M^+,\to)$. We show that the local confluence of $(X_M^+,\to)$ is sufficient for the…
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…
We propose two universal constructions of globalization of a partial action of a semigroup on a set, satisfying certain conditions which arise in Morita theory of semigroups. One of the constructions is based on the tensor product of a…
Recently E. R. Alvares, M. M. Alves and M. J. Redondo introduced a cohomology for a group $G$ with values in a module over the partial group algebra $K_{\mathrm{par}}(G)$, which is different from the partial group cohomology defined earlier…
We introduce (continuous) partial category actions on sets (topological spaces) and show that each such action admits a universal globalization. Thereby, we obtain a simultaneous generalization of corresponding results for groups, by…
We show that the category of partial modules over a Hopf algebra $H$ is a biactegory (a bimodule category) over the category of global $H$-modules. The corresponding enrichment of partial modules over global modules is described, and the…