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arXiv · 1211.1445

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

Alex Kumjian·David Pask·Aidan Sims
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Abstract

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.

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Alex Kumjian, David Pask, Aidan Sims. 2012-11-07. On the K-theory of twisted higher-rank-graph C*-algebras. https://arxiv.org/abs/1211.1445

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