有向图的$C^*$ -代数的$K$ -理论
$K$-theory of $C^*$-algebras of directed graphs
摘要：
对于有向图$E$，我们从Cuntz-Krieger生成元和关系出发，计算了$C^*$ -代数$C^*(E)$的$K$ -理论.首先计算了交叉积$C^*(E)\times_γ\IT$的$K$ -理论，然后利用对偶和Pimsner-Voiculescu正合序列计算了$C^*(E)\otimes\CK \cong (C^*(E)\times\IT)\times\IZ$的$K$ -理论.该方法依赖于分解的$C^*(E)$作为Toeplitz图$C^*$ -代数的归纳极限，由$E$的有限子图索引。证明和结果不需要对图作任何特殊的假设，并且是用图论术语给出的。如果图是用图片而不是矩阵来描述的，这会很有帮助。
英文摘要：
For a directed graph $E$, we compute the $K$-theory of the $C^*$-algebra $C^*(E)$ from the Cuntz-Krieger generators and relations. First we compute the $K$-theory of the crossed product $C^*(E)\times_γ\IT$, and then using duality and the Pimsner-Voiculescu exact sequence we compute the $K$-theory of $C^*(E)\otimes\CK \cong (C^*(E)\times\IT)\times\IZ$. The method relies on the decomposition of $C^*(E)$ as an inductive limit of Toeplitz graph $C^*$-algebras, indexed by the finite subgraphs of $E$. The proof and result require no special asssumptions about the graph, and is given in graph-theoretic terms. This can be helpful if the graph is described by pictures rather than by a matrix.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
