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Faithful Representations of Graph Algebras via Branching Systems

Published online by Cambridge University Press:  20 November 2018

Daniel Gonçalves ,
Hui Li  and
Danilo Royer
Daniel Gonçalves
Affiliation:
Departamento deMatemática -Universidade Federal de Santa Catarina, Florianópolis, 88040-900, Brazil e-mail: daemig@gmail.com
Hui Li
Affiliation:
Research Center for Operator Algebras, Department of Mathematics, East China Normal University (Minhang Campus), 500 Dongchuan Road, Minhang District, Shanghai 200241, China e-mail: hli@math.ecnu.edu.cn
Danilo Royer
Affiliation:
Departamento deMatemática -Universidade Federal de Santa Catarina, Florianópolis, 88040-900, Brazil e-mail: danilo.royer@ufsc.br
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Abstract

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We continue to investigate branching systems of directed graphs and their connections with graph algebras. We give a sufficient condition under which the representation induced from a branching system of a directed graph is faithful and construct a large class of branching systems that satisfy this condition. We finish the paper by providing a proof of the converse of the Cuntz–Krieger uniqueness theorem for graph algebras by means of branching systems.

Keywords

46L0537A55C*-algebragraph algebraLeavitt path algebrabranching systemrepresentation
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 59 , Issue 1 , 01 March 2016 , pp. 95 - 103
Copyright
Copyright © Canadian Mathematical Society 2016

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