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C*-algebras associated with presentations of subshifts ii. ideal structure and lambda-graph subsystems

Part of: Selfadjoint operator algebras Topological dynamics

Published online by Cambridge University Press:  09 April 2009

Kengo Matsumoto
Kengo Matsumoto
Affiliation:
Department of Mathematical SciencesYokohama City UniversitySeto 22-2, Kanazawa-ku Yokohama 236-0027Japan e-mail: [email protected]
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Abstract

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A λ-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 O£ associated with a λ-graph system £ from a graph theoretic view-point. If a λ-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 O£, under a certain condition on £ called (II). As a result, the class of the C*-algebras associated with λ-graph systems under condition (II) is closed under quotients by its ideals.

MSC classification

Secondary: 46L35: Classifications of $C^*$-algebras 46L05: General theory of $C^*$-algebras 37B10: Symbolic dynamics
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 81 , Issue 3 , December 2006 , pp. 369 - 385
Copyright
Copyright © Australian Mathematical Society 2006

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