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Faithful Representations of Graph Algebras via Branching Systems

Published:2015-05-21
Printed: Mar 2016
• Daniel Gonçalves,
Departamento de Matemática - Universidade Federal de Santa Catarina, Florianópolis, 88040-900, Brazil
• Hui Li,
Research Center for Operator Algebras, Department of Mathematics, East China Normal University (Minhang Campus), 500 Dongchuan Road, Minhang District, Shanghai 200241, China
• Danilo Royer,
Departamento de Matemática - Universidade Federal de Santa Catarina, Florianópolis, 88040-900, Brazil
 Format: LaTeX MathJax PDF

Abstract

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: C*-algebra, graph algebra, Leavitt path algebra, branching system, representation
 MSC Classifications: 46L05 - General theory of $C^*$-algebras 37A55 - Relations with the theory of $C^*$-algebras [See mainly 46L55]

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