埃文斯连锁综合体

arXiv - MATH - Operator Algebras Pub Date : 2024-07-08 DOI:arxiv-2407.06065

S. Joseph Lippert

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引用次数: 0

摘要

我们详细阐述了高阶图 $C^*$ 算法的埃文斯链复数构造。具体来说，我们引入了微分映射的分块矩阵表述。然后，这些分块矩阵被用来识别具有琐K理论的高阶图$C^*$数组。此外，在高阶图由一个顶点组成的特殊情况下，我们能够使用 K （"unneth"）定理来明确计算埃文斯链复数的同调群。

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On The Evans Chain Complex

We elaborate on the construction of the Evans chain complex for higher-rank graph $C^*$-algebras. Specifically, we introduce a block matrix presentation of the differential maps. These block matrices are then used to identify a wide family of higher-rank graph $C^*$-algebras with trivial K-theory. Additionally, in the specialized case where the higher-rank graph consists of one vertex, we are able to use the K\"unneth theorem to explicitly compute the homology groups of the Evans chain complex.

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arXiv - MATH - Operator Algebras

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