The $C^*$-Algebras of Arbitrary Graphs
The $C^*$-Algebras of Arbitrary Graphs
复制标题
任意图的$C^*$-代数
DOI：
10.1216/rmjm/1181069770
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发表时间：
2000
影响因子：
0.8
通讯作者：
M. Tomforde
中科院分区：
文献类型：
--
作者：
D. Drinen;M. Tomforde
在任意有向图上，我们把一个行限有向图联系起来，它的C*-代数包含原图的C*-代数作为一个满角。这使得我们可以将行有限图的C*-代数的结果推广到任意图的C*-代数：唯一性定理、简性准则、理想和本原理想空间的刻画以及图代数是AF和纯无限的条件。我们的证明只需要标准的Cuntz-Krieger技巧，而不依赖于强大的构造，如群胚、Exel-Laca代数或Cuntz-Pimsner代数。
To an arbitrary directed graph we associate a row-finite directed graph whose C*-algebra contains the C*-algebra of the original graph as a full corner. This allows us to generalize results for C*-algebras of row-finite graphs to C*-algebras of arbitrary graphs: the uniqueness theorem, simplicity criteria, descriptions of the ideals and primitive ideal space, and conditions under which a graph algebra is AF and purely infinite. Our proofs require only standard Cuntz-Krieger techniques and do not rely on powerful constructs such as groupoids, Exel-Laca algebras, or Cuntz-Pimsner algebras.