J. Aust. Math. Soc.
82 (2007), 345368

A class of limit algebras associated with directed graphs

David W. Kribs
Department of Mathematics and Statistics
University of Guelph
Guelph
Ontario N1G 2W1
Canada
dkribs@uoguelph.ca





Abstract

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 CuntzKrieger and
ToeplitzCuntzKrieger type. The limit
C*algebras determined by an increasing sequence of
positive integers, each dividing the next, are
proved to be isomorphic to CuntzPimsner algebras
and the linking maps are shown to arise as factor
maps. We derive a characterization of simplicity
and compute the
Kgroups for these algebras. We prove a
classification theorem for the class of algebras
generated by simple loop graphs.

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