On twisted higher-rank graph $C^*$-algebras
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- by Alex Kumjian, David Pask and Aidan Sims PDF
- Trans. Amer. Math. Soc. 367 (2015), 5177-5216 Request permission
Abstract:
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.References
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Additional Information
- Alex Kumjian
- Affiliation: Department of Mathematics, University of Nevada, Reno, Nevada 89557-0084
- Email: alex@unr.edu
- David Pask
- Affiliation: School of Mathematics and Applied Statistics, University of Wollongong, New South Wales 2522, Australia
- Email: dpask@uow.edu.au
- Aidan Sims
- Affiliation: School of Mathematics and Applied Statistics, University of Wollongong, New South Wales 2522, Australia
- MR Author ID: 671497
- Email: asims@uow.edu.au
- Received by editor(s): January 31, 2013
- Received by editor(s) in revised form: May 15, 2013
- Published electronically: March 3, 2015
- Additional Notes: This research was supported by the ARC. Part of the work was completed while the first author was employed at the University of Wollongong on the ARC grants DP0984339 and DP0984360.
- © Copyright 2015
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 367 (2015), 5177-5216
- MSC (2010): Primary 46L05; Secondary 18G60, 55N10
- DOI: https://doi.org/10.1090/S0002-9947-2015-06209-6
- MathSciNet review: 3335414
Dedicated: Dedicated to Marc A. Rieffel on the occasion of his 75th birthday