Ergodic Theory and Dynamical Systems



The ideal structure of Cuntz–Krieger algebras


ASTRID AN HUEF a1 and IAIN RAEBURN a2
a1 Department of Mathematics, Dartmouth College, Hanover, N.H. 03755-3551, USA
a2 Department of Mathematics, University of Newcastle, N.S.W. 2308, Australia

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 ${\cal {AO}}_A$.

(Received October 28 1994)
(Revised May 7 1996)



Footnotes

This research was supported by the Australian Research Council.