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

2012/05/15 by Hui Li, Li, Hui, David Pask +3
Mathematics · Physics and Astronomy · #46L05 #Advanced Operator Algebra Research #FOS: Mathematics #Noncommutative and Quantum Gravity Theories #Operator Algebras (math.OA) #Quantum Electrodynamics and Casimir Effect

paper · pdf · doi:10.48550/arxiv.1205.3264

openalex publication_date 2012/05/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

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^∞.

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