Simplicity of twisted $C^{\ast }$-algebras of higher-rank graphs and crossed products by quasifree actions

Abstract

We characterise simplicity of twisted $C^{\ast }$-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.