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arXiv 1102.1229math.OA
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高秩图的道路空间

The path space of a higher-rank graph

Samuel B. G. Webster

备注：
30 pages, all figures drawn with TikZ/PGF. Updated numbering and minor corrections to coincide with published version. Updated 29-Feb-2012 to fix a compiling error which resulted in the arXiv PDF output containing two copies of the article
发表信息：
Studia Math. 204 (2011), 155-185
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摘要：

本文构造了一个局部紧的Hausdorff拓扑，它是关于一个非对齐的$k$ -图$Λ$的道路空间的.我们把边界道路空间$\partialΛ$定义为$C^*(Λ)$的交换$C^*$ -子代数$D_Λ$的谱.然后，使用一个类似于Farthing的结构，我们构造了一个无源的$k$ -图$\wtΛ$，其中$Λ$被嵌入，并证明了$\partialΛ$是同胚的$\partial\wtΛ$的一个子集。我们证明了当$Λ$是行有限的，我们可以识别$C^*(Λ)$与$C^*(\wtΛ)$的一个完整的角，并推导出$D_Λ$同构于$D_{\wtΛ}$的一个角。最后，我们证明了这种同构实现了边界-路空间之间的同胚.

英文摘要：

We construct a locally compact Hausdorff topology on the path space of a finitely aligned $k$-graph $Λ$. We identify the boundary-path space $\partialΛ$ as the spectrum of a commutative $C^*$-subalgebra $D_Λ$ of $C^*(Λ)$. Then, using a construction similar to that of Farthing, we construct a finitely aligned $k$-graph $\wtΛ$ with no sources in which $Λ$ is embedded, and show that $\partialΛ$ is homeomorphic to a subset of $\partial\wtΛ$ . We show that when $Λ$ is row-finite, we can identify $C^*(Λ)$ with a full corner of $C^*(\wtΛ)$, and deduce that $D_Λ$ is isomorphic to a corner of $D_{\wtΛ}$. Lastly, we show that this isomorphism implements the homeomorphism between the boundary-path spaces.

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。

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