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Description of partial actions [PDF]

Sao Paulo Journal of Mathematical Sciences, 2021
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 decomposed as product of indecomposable algebras and we give a description of the partial actions of groups on these ...
Wagner Cortes, Eduardo N Marcos
exaly   +3 more sources

Partial Actions and Power Sets [PDF]

International Journal of Mathematics and Mathematical Sciences, 2013
We consider a partial action (X,α) with enveloping action (T,β). In this work we extend α to a partial action on the ring (P(X),Δ,∩) and find its enveloping action (E,β).
Jesús Ávila, João Lazzarin
doaj   +3 more sources

Enveloping Actions for Partial Hopf Actions [PDF]

Communications in Algebra, 2010
Motivated by partial group actions on unital algebras, in this article we extend many results obtained by Exel and Dokuchaev to the context of partial actions of Hopf algebras, according to Caenepeel and Jansen. First, we generalize the theorem about the existence of an enveloping action, also known as the globalization theorem.
Eliezer Batista
exaly   +3 more sources

Decomposable partial actions [PDF]

Journal of Functional Analysis, 2021
We define the decomposition property for partial actions of discrete groups on $C^*$-algebras. Decomposable partial systems appear naturally in practice, and many commonly occurring partial actions can be decomposed into partial actions with the decomposition property.
Shirly Geffen, Fernando Abadie, Eusebio Gardella   +2 more
exaly   +3 more sources

Partial actions and partial skew group rings

Journal of Algebra, 2008
This paper extends several classical results to partial skew group rings. A partial action of a group on an algebra is a collection of ideals \(D_g\) and isomorphisms \(\alpha_g\colon D_g\to D_{g^{-1}}\) satisfying some natural constraints. A partial skew group ring is the set of all finite formal sums \(\sum_ga_gu_g\) with \(a_g\) from the ideal \(D_g\
MIGUEL Ferrero
exaly   +3 more sources

Enveloping actions and Takai duality for partial actions

Journal of Functional Analysis, 2003
We show that any continuous partial action on a topological space has a unique enveloping action, i.e. it is the restriction of a global action. In the case of C^*-algebras we prove that any partial action has an enveloping action up to Morita equivalence.
Fernando Abadie
exaly   +3 more sources

Partial Actions on Categories [PDF]

Communications in Algebra, 2016
In this paper we introduce the definition of partial action on small $k$-categories generalizing the similar well known notion of partial actions on algebras. The point of view of partial action which we use in this paper is the one which was introduced by Exel in his work on $C^*$-algebras, see \cite{E}.
Wagner Cortes, Eduardo N Marcos, MIGUEL Ferrero   +2 more
exaly   +3 more sources

Partial actions and subshifts

Journal of Functional Analysis, 2017
Given a finite alphabet $Λ$, and a not necessarily finite type subshift $X\subseteq Λ^\infty$, we introduce a partial action of the free group $F(Λ)$ on a certain compactification $Ω_X$ of $X$, which we call the spectral partial action. The space $Ω_X$ has already appeared in many papers in the subject, arising as the spectrum of a commutative C ...
Mikhailo Dokuchaev
exaly   +4 more sources

Partial semigroupoid actions on sets

Semigroup Forum
We introduce partial semigroupoid actions on sets and demonstrate that each such action admits universal globalization. Our construction extends the universal globalization for partial category actions given by P. Nystedt (Lundström) and the tensor product globalization for strong partial semigroup actions given by G. Kudryavtseva and V.
Thaisa Tamusiunas
exaly   +3 more sources

Galois correspondence for partial groupoid actions

Communications in Algebra
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Thaisa Tamusiunas
exaly   +3 more sources