On The Evans Chain Complex
Operator Algebras
2025-05-14 v1
Abstract
We elaborate on the construction of the Evans chain complex for higher-rank graph -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 -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.
Keywords
Cite
@article{arxiv.2407.06065,
title = {On The Evans Chain Complex},
author = {S. Joseph Lippert},
journal= {arXiv preprint arXiv:2407.06065},
year = {2025}
}