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A Class of Limit Algebras Associated with Directed Graphs

Part of: Selfadjoint operator algebras Linear spaces and algebras of operators

Published online by Cambridge University Press:  09 April 2009

David W. Kribs  and
Baruch Solel
David W. Kribs
Affiliation:
Department of Mathematics and Statistics, University of Guelph, Guelph, Ontario NIG 2W1, [email protected]
Baruch Solel
Affiliation:
Department of Mathematics, Technion – Israel Institute of Technology, Haifa 32000, [email protected]
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Abstract

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Every directed graph defines a Hilbert space and a family of weighted shifts that act on the space. We identify a natural notion of periodicity for such shifts and study their C* -algebras. We prove the algebras generated by all shifts of a fixed period are of Cuntz-Krieger and Toeplitz-Cuntz-Krieger type. The limit C* -algebras determined by an increasing sequence of positive integers, each dividing the next, are proved to be isomorphic to Cuntz-Pimsner algebras and the linking maps are shown to arise as factor maps. We derive a characterization of simplicity and compute the K-groups for these algebras. We prove a classification theorem for the class of algebras generated by simple loop graphs.

MSC classification

Secondary: 46L05: General theory of $C^*$-algebras 47L40: Limit algebras, subalgebras of $C^*$-algebras
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 82 , Issue 3 , June 2007 , pp. 345 - 368
Copyright
Copyright © Australian Mathematical Society 2007

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