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

@article{Katsura2006ACO,
  title={A class of \$\{C^*\}\$-algebras generalizing both graph algebras and homeomorphism \$\{C^*\}\$-algebras III, ideal structures},
  author={Takeshi Katsura},
  journal={Ergodic Theory and Dynamical Systems},
  year={2006},
  volume={26},
  pages={1805 - 1854}
}
  • Takeshi Katsura
  • Published 14 August 2004
  • Mathematics
  • Ergodic Theory and Dynamical Systems
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… Expand
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