English
Related papers

Related papers: Groupoid Twisted Partial Actions

200 papers

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…

Rings and Algebras · Mathematics 2026-04-24 Mikhailo Dokuchaev , Emmanuel Jerez , José L. Vilca-Rodríguez

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…

Rings and Algebras · Mathematics 2022-03-31 Paolo Saracco , Joost Vercruysse

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…

Dynamical Systems · Mathematics 2026-04-14 Chris Bruce , Xin Li

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.…

Representation Theory · Mathematics 2018-10-09 Eneilson Campos , Grasiela Martini , Graziela Fonseca

We generalize Exel's notion of partial group action to monoids. For partial monoid actions that can be defined by means of suitably well-behaved systems of generators and relations, we employ classical rewriting theory in order to describe…

General Topology · Mathematics 2007-05-23 Michael Megrelishvili , Lutz Schroeder

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 assure the existence of enveloping actions. This allows…

Rings and Algebras · Mathematics 2009-10-08 Marcelo Muniz S. Alves , Eliezer Batista

Given a smooth partial action $\alpha$ of a Lie groupoid $G$ on a smooth manifold $M,$ we provide necessary and sufficient conditions for $\alpha$ to be globalizable with smooth globalization. As an application, we provide results on the…

Differential Geometry · Mathematics 2024-12-31 Víctor Marín , Héctor Pinedo , J. L. V. Rodríguez

Given a group $G$ and a partial factor set $\sigma $ of $G,$ we introduce the twisted partial group algebra $\kappa_{par}^{\sigma}G,$ which governs the partial projective $\sigma$-representations of $G$ into algebras over a filed $\kappa.$…

Rings and Algebras · Mathematics 2023-11-29 Mikhailo Dokuchaev , Emmanuel Jerez

Transformational music theory is a recent field in music theory which studies the possible transformations between musical objects, such as chords. In the framework of the theory initiated by David Lewin, the set of all transformations…

Group Theory · Mathematics 2018-01-11 Alexandre Popoff

In this work we investigate the notion of action or coaction of a finite quantum groupoid in von Neumann algebras context. In particular we prove a double crossed product theorem and prove the existence of an universal von Neumann algebra…

Quantum Algebra · Mathematics 2007-05-23 Jean-Michel Vallin

A Lie groupoid can be thought of as a generalization of a Lie group in which the multiplication is only defined for certain pairs of elements. From another perspective, Lie groupoids can be regarded as manifolds endowed with a type of…

Differential Geometry · Mathematics 2023-09-26 Henrique Bursztyn , Matias del Hoyo

Given a partial action \alpha of a group G on an associative algebra A we consider the crossed product A x_\alpha G. Using the algebras of multipliers of ideals of A we prove that A x_\alpha G is associative, provided that all ideals of A…

Rings and Algebras · Mathematics 2010-03-16 M. Dokuchaev , R. Exel

A semi-projective representation is a homomorphism of a finite group into the group of semi-projective transformations of a finite dimensional vector space over a field. Schur's concept of a representation group for projective…

Group Theory · Mathematics 2023-05-05 Massimiliano Alessandro , Christian Gleissner , Julia Kotonski

For a free partial action of a group in a set we realize the associated partial skew group ring as an algebra of functions with finite support over an equivalence relation and we use this result to characterize the ideals in the partial…

Rings and Algebras · Mathematics 2013-06-18 Viviane M. Beuter , Daniel Gonçalves

Given a partial action of a topological group $G$ on a space $X$, we determine properties $\mathcal P$ which can be extended from $X$ to its globalization. We treat the cases when $\mathcal P$ is any of the following: Hausdorff, regular,…

General Topology · Mathematics 2023-12-21 L. Martínez , H. Pinedo , A. Villamizar

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…

Rings and Algebras · Mathematics 2015-05-20 Felipe Castro , Antonio Paques , Glauber Quadros , Alveri Sant'Ana

In 1990, Rieffel defined a notion of proper action of a group $H$ on a $C^*$-algebra $A$. He then defined a generalized fixed point algebra $A^{\alpha}$ for this action and showed that $A^{\alpha}$ is Morita equivalent to an ideal of the…

Operator Algebras · Mathematics 2009-08-03 Jonathan Henry Brown

This article explores the novel notion of gyrogroup actions, which is a natural generalization of the usual notion of group actions. As a first step toward the study of gyrogroup actions from the algebraic viewpoint, we prove three…

Group Theory · Mathematics 2016-02-05 Teerapong Suksumran

The notions of Busby-Smith and Green type twisted actions are extended to discrete unital inverse semigroups. The connection between the two types, and the connection with twisted partial actions, are investigated. Decomposition theorems…

funct-an · Mathematics 2007-05-23 Nandor Sieben

We introduce a new notion of twisted actions of inverse semigroups and show that they correspond bijectively to certain regular Fell bundles over inverse semigroups, yielding in this way a structure classification of such bundles. These…

Operator Algebras · Mathematics 2014-02-26 Alcides Buss , Ruy Exel