Abstract
We classify graph C *-algebras, namely, Cuntz-Krieger algebras associated to the Bass-Hashimoto edge incidence operator of a finite graph, up to strict isomorphism. This is done by a purely graph theoretical calculation of the K-theory of the C *-algebras and the method also provides an independent proof of the classification up to Morita equivalence and stable equivalence of such algebras, without using the boundary operator algebra. A direct relation is given between the K 1-group of the algebra and the cycle space of the graph.
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We thank Jakub Byszewski for his input in Sect. 2.8. The position of the unit in K 0( \({\mathcal{O}}\) Ч) was guessed based on some example calculations by Jannis Visser in his SCI 291 Science Laboratory at Utrecht University College.
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Cornelissen, G., Lorscheid, O. & Marcolli, M. On the K-Theory of Graph C *-Algebras. Acta Appl Math 102, 57–69 (2008). https://doi.org/10.1007/s10440-008-9208-4
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DOI: https://doi.org/10.1007/s10440-008-9208-4