Twisted k-Graph Algebras Associated to Bratteli Diagrams

@article{Pask2014TwistedKA,
  title={Twisted k-Graph Algebras Associated to Bratteli Diagrams},
  author={David Pask and Adam Sierakowski and Aidan Sims},
  journal={Integral Equations and Operator Theory},
  year={2014},
  volume={81},
  pages={375-408}
}
Given a system of coverings of k-graphs, we show that the second cohomology of the resulting (k + 1)-graph is isomorphic to that of any one of the k-graphs in the system, and compute the semifinite traces of the resulting twisted (k + 1)-graph C*-algebras. 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 of the resulting twisted 3-graph C*-algebras. We deduce that every such… 
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