On the representations of Leavitt path algebras.
type: Item
instance of: scholarly article
title: On the representations of Leavitt path algebras.
zbMATH Open document ID: 1235.16014
author: Daniel Gonçalves
author: Danilo Royer
published in: Journal of Algebra
publication date: 2011-12-08T00:00:00Z
full work available at URL: https://arxiv.org/abs/1006.2797
review text: In a paper by the same authors [see Graph algebras as subalgebras of the bounded operators in \(L_2(\mathbb R)\), \url{http://arxiv.org/abs/0908.1055v1}], they started the study of representations of graph \(C^*\)-algebras using branching systems. There, it is proved that, for a large class of graph \(C^*\)-algebras, all representations of such algebras are unitarily equivalent to representations arising from branching systems. In the paper under review the same authors introduce the \(E\)-algebraic branching systems and study how these objects induce gradings of the associated Leavitt path algebra. They prove the existence of these systems and give conditions which imply the faithfulness of the induced representations. On the other hand they study the following problem: given a representation of a Leavitt path algebra, how can we find a representation induced by an \(E\)-algebraic branching system equivalent to a restriction of the original representation?
reviewed by: Candido Martín González
Mathematics Subject Classification ID: 16S88
Mathematics Subject Classification ID: 16G20
Mathematics Subject Classification ID: 46L05
zbMATH DE Number: 5987867
zbMATH Keywords: Leavitt path algebras
zbMATH Keywords: graph \(C^*\)-algebras
zbMATH Keywords: induced representations
zbMATH Keywords: algebraic branching systems
MaRDI profile type: Publication
OpenAlex ID: W2963603892
arXiv ID: 1006.2797
cites work: The Leavitt path algebra of a graph.
cites work: Purely infinite simple Leavitt path algebras.
cites work: Module theory over Leavitt path algebras and \(K\)-theory.
cites work: Perron-Frobenius operators and representations of the Cuntz-Krieger algebras for infinite matrices
cites work: Uniqueness theorems and ideal structure for Leavitt path algebras
DOI: 10.1016/J.JALGEBRA.2011.02.034
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description: scientific article