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Search: MSC category 37A55 ( Relations with the theory of $C^$-algebras [See mainly 46L55] *$-algebras [See mainly 46L55] * )

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Gonçalves, Daniel; Li, Hui; Royer, Danilo
Faithful representations of graph algebras via branching systems
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
Categories:46L05, 37A55

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