J. Aust. Math. Soc.
82 (2007), 345-368
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A class of limit algebras associated with directed graphs
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David W. Kribs
Department of Mathematics and Statistics
University of Guelph
Guelph
Ontario N1G 2W1
Canada
dkribs@uoguelph.ca
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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.
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Australian Mathematical Publishing Association Inc.
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©
Australian MS
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