J. Aust. Math. Soc.
81 (2006), 369385

C*algebras associated with presentations of subshifts II. Ideal structure and lambdagraph subsystems

Kengo Matsumoto
Department of Mathematical Sciences
Yokohama City University
Seto 222, Kanazawaku
Yokohama 2360027
Japan
kengo@yokohamacu.ac.jp



Abstract

A
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
C*algebra
associated with a
graph system
from a graph theoretic viewpoint. If a
graph system comes from a finite labeled graph,
the algebra becomes a CuntzKrieger 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.

Download the article in PDF format (size 169 Kb)


Australian Mathematical Publishing Association Inc.

©
Australian MS

