A class of C^*-algebras generalizing both graph algebras and homeomorphism C^*-algebras III, ideal structures

Details A class of C^*-algebras generalizing both graph algebras and homeomorphism C^*-algebras III, ideal structures A class of C^*-algebras generalizing both graph algebras and homeomorphism C^*-algebras III, ideal structures

2004-08-14

arxiv.org/abs/math/0408190v2

Mathematics

Operator Algebras

47 pages, typos corrected, Sections 11 and 12 Changed

Scientific paper

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 so-called 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.

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