J. Aust. Math. Soc.
81 (2006), 369-385|
C*-algebras associated with presentations of subshifts II. Ideal structure and lambda-graph subsystems
Department of Mathematical Sciences
Yokohama City University
Seto 22-2, Kanazawa-ku
-graph system is a labeled Bratteli diagram with
shift transformation. It is a generalization of
finite labeled graphs and presents a subshift.
In Doc. Math. 7 (2002) 1–30, the
author constructed a
associated with a
from a graph theoretic view-point. If a
-graph system comes from a finite labeled graph,
the algebra becomes a Cuntz-Krieger algebra. In
this paper, we prove that there is a bijective
correspondence between the lattice of all
saturated hereditary subsets of
and the lattice of all ideals of the algebra
, under a certain condition on
called (II). As a result, the class of the
C*-algebras associated with
-graph systems under condition (II) is closed
under quotients by its ideals.
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