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

作者：Li Hui^*; Pask David; Sims Aidan

来源：The New York Journal of Mathematics, 2014, 20: 447-469.

• C*-algebra
• graph algebra
• C*-correspondence
• topological graph
• Cuntz Pimsner algebra

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 is isomorphic to the Toeplitz algebra of Katsura%26apos;s topological-graph bimodule, and that the C*-algebra generated by a universal covariant representation of E is isomorphic to Katsura%26apos;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 the infinite-path space E-infinity

• 出版日期2014