Partial projective representations and partial actions.
type: Item
instance of: scholarly article
title: Partial projective representations and partial actions.
zbMATH Open document ID: 1211.20016
author: B. V. Novikov
author: Michael Dokuchaev
published in: Journal of Pure and Applied Algebra
publication date: 2009-11-25T00:00:00Z
review text: The purpose of the present article is to define partial projective representations of groups in analogy with the classical representation theory. This notion is closely connected with the notions twisted partial products and twisted partial actions [see \textit{M. Dokuchaev}, \textit{R. Exel} and \textit{J. J. Simón}, J. Algebra 320, No. 8, 3278-3310 (2008; Zbl 1160.16016)]. First, the authors give the necessary information about projective representations of semigroups and their factor sets [see \textit{B. V. Novikov}, Dopov. Akad. Nauk Ukr. RSR, Ser. A 1979, 472-475 (1979; Zbl 0411.20047)]. After that they define equivalent factor sets, product of factor sets and Schur multiplier of a semigroup with identity. So the authors define partial projective representations of a group by means of projective representations of a semigroup which is associated with the group. It is given another definition, which is independent of semigroups. Later in the paper is studied the structure of the factor sets of partial projective representations. The connections between the projective partial representations and the twisted partial actions are also investigated.
reviewed by: S. V. Mihovski
Mathematics Subject Classification ID: 20C25
Mathematics Subject Classification ID: 20M30
Mathematics Subject Classification ID: 16S35
zbMATH DE Number: 5638331
zbMATH Keywords: representations of semigroups
zbMATH Keywords: partial projective representations of groups
zbMATH Keywords: Schur multipliers
zbMATH Keywords: factor sets
zbMATH Keywords: twisted partial actions
MaRDI profile type: Publication
full work available at URL: j.jpaa.2009.05.001
OpenAlex ID: W2111399414
cites work: Partial actions of groups and actions of inverse semigroups
cites work: Characterisations of crossed products by partial actions
cites work: Partial representations and partial group algebras
cites work: On finite degree partial representations of groups.
cites work: Partial dynamical systems and C*-algebras generated by partial isometries
cites work: Associativity of crossed products by partial actions, enveloping actions and partial representations
cites work: PARTIAL ACTIONS OF GROUPS
cites work: Circle actions on \(C^*\)-algebras, partial automorphisms, and a generalized Pimsner-Voiculescu exact sequence
cites work: \(K\)-theory for partial crossed products by discrete groups
cites work: Twisted Partial Actions: A Classification of Regular C*-Algebraic Bundles
cites work: A class of C*-algebras and topological Markov chains
cites work: Cuntz-Krieger algebras for infinite matrices
cites work: Crossed products by twisted partial actions and graded algebras.
cites work: Q4198946
cites work: Extending Multipliers from Semigroups
cites work: Extensions of multipliers and dilations of projective isometric representations
cites work: Q4126563
cites work: Q3853833
cites work: Semigroup cohomology and applications
cites work: A note on Birget-Rhodes expansion of groups
DOI: 10.1016/J.JPAA.2009.05.001
description: scientific article; zbMATH DE number 5638331