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The ideal structure of Cuntz–Krieger algebras

Published online by Cambridge University Press:  01 June 1997

ASTRID AN HUEF  and
IAIN RAEBURN
ASTRID AN HUEF
Affiliation:
Department of Mathematics, Dartmouth College, Hanover, N.H. 03755-3551, USA
IAIN RAEBURN
Affiliation:
Department of Mathematics, University of Newcastle, N.S.W. 2308, Australia
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Abstract

We construct a universal Cuntz–Krieger algebra ${\cal {AO}}_A$, which is isomorphic to the usual Cuntz–Krieger algebra ${\cal O}_A$ when $A$ satisfies condition $(I)$ of Cuntz and Krieger. The Cuntz classification of ideals in ${\cal O}_A$ when $A$ satisfies condition $(II)$ extends to a classification of the gauge invariant ideals in ${\cal {AO}}_A$. We use this to describe the topology on the primitive ideal space of ${\cal {AO}}_A$.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 17 , Issue 3 , June 1997 , pp. 611 - 624
Copyright
1997 Cambridge University Press

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Footnotes

This research was supported by the Australian Research Council.