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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.
S. Joseph Lippert (Mon,) studied this question.
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