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
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DOI：
10.1017/s0143385706000320
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发表时间：
2004-08
影响因子：
0.9
通讯作者：
Takeshi Katsura
中科院分区：
文献类型：
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作者：
Takeshi Katsura
研究了由拓扑图产生的$C^*$-代数的理想结构。我们给出了这类$C^*-代数在所谓规范作用下不变的理想的完整刻画，并给出了拓扑图上使所有理想在规范作用下不变的一个条件。我们得到了我们的$C^*$-代数是单的、素数的或本原的条件。我们完全确定了素数理想，并证明了它们中的大多数都是原始的。最后，我们构造了一个离散图，它的相关的$C^*$-代数是素数但不是本原的。
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.