Abstract

We develop notions of a representation of a topological graph E and of a covariant representation of a topological graph E which do not require the machinery of C*correspondences and CuntzPimsner algebras. We show that the C*algebra generated by a universal representation of E is isomorphic to the Toeplitz algebra of Katsura's topologicalgraph bimodule, and that the C*algebra generated by a universal covariant representation of E is isomorphic to Katsura's topological graph C*algebra. We exhibit our results by constructing the isomorphism between the C*algebra of a rowfinite directed graph E with no sources and the C*algebra of the topological graph arising from the shift map acting on the infinitepath space E∞.