Skip to main content
placeholder image

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

Journal Article


Download full-text (Open Access)

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 is isomorphic to the Toeplitz algebra of Katsura's topological-graph 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 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∞.

Publication Date


  • 2014

Citation


  • Li, H., Pask, D. & Sims, A. (2014). An elementary approach to C*-algebras associated to topological graphs. The New York Journal of Mathematics, 20 447-469.

Scopus Eid


  • 2-s2.0-84901192699

Ro Full-text Url


  • http://ro.uow.edu.au/cgi/viewcontent.cgi?article=4239&context=eispapers

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/3223

Number Of Pages


  • 22

Start Page


  • 447

End Page


  • 469

Volume


  • 20

Place Of Publication


  • http://nyjm.albany.edu/j/2014/20-26.html

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 is isomorphic to the Toeplitz algebra of Katsura's topological-graph 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 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∞.

Publication Date


  • 2014

Citation


  • Li, H., Pask, D. & Sims, A. (2014). An elementary approach to C*-algebras associated to topological graphs. The New York Journal of Mathematics, 20 447-469.

Scopus Eid


  • 2-s2.0-84901192699

Ro Full-text Url


  • http://ro.uow.edu.au/cgi/viewcontent.cgi?article=4239&context=eispapers

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/3223

Number Of Pages


  • 22

Start Page


  • 447

End Page


  • 469

Volume


  • 20

Place Of Publication


  • http://nyjm.albany.edu/j/2014/20-26.html