On twisted higher-rank graph C*-algebras

  title={On twisted higher-rank graph C*-algebras},
  author={Alex Kumjian and David Pask and Aidan Sims},
  journal={Transactions of the American Mathematical Society},
We define the categorical cohomology of a k-graphand show that the first three terms in this cohomology are isomorphic to the corresponding terms in the cohomology defined in our previous paper. This leads to an alternative characterisation of the twisted k-graph C � -algebras introduced there. We prove a gauge-invariant uniqueness theorem and use it to show that every twisted k-graph C � -algebra is isomorphic to a twisted groupoid C � -algebra. We deduce criteria for simplicity, prove a Cuntz… 

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