埃文斯连锁综合体

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。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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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