A class of C^*algebras generalizing both graph algebras and homeomorphism C^*algebras III, ideal structures
Abstract
We investigate the ideal structures of the C^*algebras arising from topological graphs. We give the complete description of ideals of such C^*algebras which are invariant under the socalled gauge action, and give the condition on topological graphs so that all ideals are invariant under the gauge action. We get conditions for our C^*algebras to be simple, prime or primitive. We completely determine the prime ideals, and show that most of them are primitive. Finally, we construct a discrete graph such that the associated C^*algebra is prime but not primitive.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 August 2004
 arXiv:
 arXiv:math/0408190
 Bibcode:
 2004math......8190K
 Keywords:

 Mathematics  Operator Algebras;
 Mathematics  Dynamical Systems;
 Primary 46L05;
 Secondary 46L55;
 37B99
 EPrint:
 47 pages, typos corrected, Sections 11 and 12 Changed