On twisted higher-rank graph C*-algebras

Details On twisted higher-rank graph C*-algebras On twisted higher-rank graph C*-algebras

2011-12-29

arxiv.org/abs/1112.6233v1

Mathematics

Operator Algebras

37 pages, pictures prepared using TiKZ

Scientific paper

We define the categorical cohomology of a k-graph \Lambda\ and 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-Krieger uniqueness theorem and establish that all twisted k-graph C*-algebras are nuclear and belong to the bootstrap class.

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