Geodesic
Faithful Representations of Graph Algebras via Branching Systems
Canadian mathematical bulletin, Tome 59 (2016) no. 1, pp. 95-103

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DOI

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.
DOI : 10.4153/CMB-2015-032-x
Mots-clés : 46L05, 37A55, C*-algebra, graph algebra, Leavitt path algebra, branching system, representation 
Gonçalves, Daniel; Li, Hui; Royer, Danilo. Faithful Representations of Graph Algebras via Branching Systems. Canadian mathematical bulletin, Tome 59 (2016) no. 1, pp. 95-103. doi: 10.4153/CMB-2015-032-x
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     title = {Faithful {Representations} of {Graph} {Algebras} via {Branching} {Systems}},
     journal = {Canadian mathematical bulletin},
     pages = {95--103},
     year = {2016},
     volume = {59},
     number = {1},
     doi = {10.4153/CMB-2015-032-x},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2015-032-x/}
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