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

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Abstract

We investigate the ideal structures of the C*-algebras arising from topological graphs. We give a complete description of ideals of such C*-algebras that are invariant under the so-called gauge action, and give a 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 for which the associated C*-algebra is prime but not primitive.

Original languageEnglish
Pages (from-to)1805-1854
Number of pages50
JournalErgodic Theory and Dynamical Systems
Volume26
Issue number6
DOIs
Publication statusPublished - 2006 Dec
Externally publishedYes

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ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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