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On the K-Theory of Graph C^∗-Algebras

Cornelissen, Gunther and Lorscheid, Oliver and Marcolli, Matilde (2008) On the K-Theory of Graph C^∗-Algebras. Acta Applicandae Mathematicae, 102 (1). pp. 57-69. ISSN 0167-8019. doi:10.1007/s10440-008-9208-4.

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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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Additional Information:© 2008 Springer Science. Received: 12 November 2007/ Accepted: 9 January 2008/Published online: 25 January 2008. We thank Jakub Byszewski for his input in Sect. 2.8. The position of the unit in K0(OY) was guessed based on some example calculations by Jannis Visser in his SCI 291 Science Laboratory at Utrecht University College.
Subject Keywords:graph C^*-algebras; K-theory; edge incidence operator; Morita equivalence; strict isomorphism
Issue or Number:1
Record Number:CaltechAUTHORS:CORaam08
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:13484
Deposited By: Ruth Sustaita
Deposited On:16 Jun 2009 18:06
Last Modified:08 Nov 2021 22:38

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