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arXiv · 1205.3264

An elementary approach to C*-algebras associated to topological graphs

Hui Li·David Pask·Aidan Sims
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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 Cuntz-Pimsner algebras. We show that the C*-algebra generated by a universal representation of E coincides with the Toeplitz algebra of Katsura's topological-graph bimodule, and that the C*-algebra generated by a universal covariant representation of E coincides with Katsura's topological graph C*-algebra. We exhibit our results by constructing the isomorphism between the C*-algebra of a row-finite directed graph E with no sources and the C*-algebra of the topological graph arising from the shift map acting on infinite path space E^\infty.

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Hui Li, David Pask, Aidan Sims. 2012-05-15. An elementary approach to C*-algebras associated to topological graphs. https://arxiv.org/abs/1205.3264

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