On the representations of Leavitt path algebras.
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?
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