Simplicity of twisted -algebras of higher-rank graphs and crossed products by quasifree actions
Alex Kumjian
University of Nevada Reno, USADavid Pask
University of Wollongong, AustraliaAidan Sims
University of Wollongong, Australia
![Simplicity of twisted $C^*$-algebras of higher-rank graphs and crossed products by quasifree actions cover](/_next/image?url=https%3A%2F%2Fcontent.ems.press%2Fassets%2Fpublic%2Fimages%2Fserial-issues%2Fcover-jncg-volume-10-issue-2.png&w=3840&q=90)
Abstract
We characterise simplicity of twisted -algebras of row-finite -graphs with no sources. We show that each 2-cocycle on a cofinal -graph determines a canonical second-cohomology class for the periodicity group of the graph. The groupoid of the -graph then acts on the cartesian product of the infinite-path space of the graph with the dual group of the centre of any bicharacter representing this second-cohomology class. The twisted k-graph algebra is simple if and only if this action is minimal. We apply this result to characterise simplicity for many twisted crossed products of -graph algebras by quasifree actions of free abelian groups.
Cite this article
Alex Kumjian, David Pask, Aidan Sims, Simplicity of twisted -algebras of higher-rank graphs and crossed products by quasifree actions. J. Noncommut. Geom. 10 (2016), no. 2, pp. 515–549
DOI 10.4171/JNCG/241