A class of limit algebras associated with directed graphs

Details A class of limit algebras associated with directed graphs A class of limit algebras associated with directed graphs

2004-11-17

arxiv.org/abs/math/0411379v1

J. Aust. Math. Soc., 82 (2007), 1-24.

Mathematics

Operator Algebras

31 pages, preprint version

Scientific paper

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.

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