On the K-theory of twisted higher-rank-graph C∗-algebras

We investigate the K-theory of twisted higher-rank-graph algebras by adapting parts of Elliott’s computation of the K-theory of the rotation algebras. We show that each 2-cocycle on a higher-rank graph taking values in an abelian group determines a continuous bundle of twisted higher-rank graph alge...

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Bibliographic Details
Published in:Journal of mathematical analysis and applications 2013-05, Vol.401 (1), p.104-113
Main Authors: Kumjian, Alex, Pask, David, Sims, Aidan
Format: Article
Language:English
Subjects:
[formula omitted]-algebra
[formula omitted]-graph
[formula omitted]-theory
Graph algebra
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Summary:We investigate the K-theory of twisted higher-rank-graph algebras by adapting parts of Elliott’s computation of the K-theory of the rotation algebras. We show that each 2-cocycle on a higher-rank graph taking values in an abelian group determines a continuous bundle of twisted higher-rank graph algebras over the dual group. We use this to show that for a circle-valued 2-cocycle on a higher-rank graph obtained by exponentiating a real-valued cocycle, the K-theory of the twisted higher-rank graph algebra coincides with that of the untwisted one.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2012.11.030