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arXiv · 1403.4324

Twisted k-graph algebras associated to Bratteli diagrams

David Pask·Adam Sierakowski·Aidan Sims
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Abstract

Given a system of coverings of k-graphs, we show that the cohomology of the resulting (k+1)-graph is isomorphic to that of any one of the k-graphs in the system. We then consider Bratteli diagrams of 2-graphs whose twisted C*-algebras are matrix algebras over noncommutative tori. For such systems we calculate the ordered K-theory and the gauge-invariant semifinite traces of the resulting 3-graph C*-algebras. We deduce that every simple C*-algebra of this form is Morita equivalent to the C*-algebra of a rank-2 Bratteli diagram in the sense of Pask-Raeburn-Rørdam-Sims.

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David Pask, Adam Sierakowski, Aidan Sims. 2014-03-18. Twisted k-graph algebras associated to Bratteli diagrams. https://arxiv.org/abs/1403.4324

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