Simplicity of twisted C*-algebras of higher-rank graphs and crossed products by quasifree actions

Abstract

We characterise simplicity of twisted C*-algebras of row-finite k-graphs with no sources. We show that each 2-cocycle on a cofinal k-graph determines a canonical second-cohomology class for the periodicity group of the graph. The groupoid of the k-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 k-graph algebras by quasifree actions of free abelian groups.

26 pages; diagrams prepared using TikZ. V2: numerous typographical errors corrected. Example 6.4 expanded and improved, on the suggestion of a helpful referee. Thanks to both the referee and to Becky Armstrong for their comments and corrections. This version matches the version that will appear in J. Noncommutative Geometry