A Class of C∗-algebras Generalizing Both Graph Algebras and Homeomorphism C∗-algebras Iii, Ideal Structures
نویسنده
چکیده
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.
منابع مشابه
A Class of C * -algebras Generalizing Both Graph Algebras and Homeomorphism C
We introduce a new class of C∗-algebras, which is a generalization of both graph algebras and homeomorphism C∗-algebras. This class is very large and also very tractable. We prove the so-called gauge-invariant uniqueness theorem and the CuntzKrieger uniqueness theorem, and compute the K-groups of our algebras.
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We introduce a new class of C∗-algebras, which is a generalization of both graph algebras and homeomorphism C∗-algebras. This class is very large and also very tractable. We prove the so-called gauge-invariant uniqueness theorem and the Cuntz-Krieger uniqueness theorem, and compute the K-groups of our algebras.
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