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

Takeshi Katsura

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

Operator Algebras 2007-05-23 v2 Dynamical Systems

Authors: Takeshi Katsura

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 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.

Keywords

C*-algebras topological graphs gauge action ideal structure prime ideals primitive ideals

Cite

@article{arxiv.math/0408190,
  title  = {A class of C^*-algebras generalizing both graph algebras and homeomorphism C^*-algebras III, ideal structures},
  author = {Takeshi Katsura},
  journal= {arXiv preprint arXiv:math/0408190},
  year   = {2007}
}

Comments

47 pages, typos corrected, Sections 11 and 12 Changed