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

TL;DR

This paper characterizes when twisted C*-algebras of higher-rank graphs are simple, linking algebraic properties to groupoid actions and applying results to crossed products by quasifree actions.

Contribution

It provides a new criterion for simplicity of twisted k-graph C*-algebras based on minimality of a groupoid action, extending to crossed products by quasifree actions.

Findings

Simplicity is characterized by minimality of a specific groupoid action.

A canonical second-cohomology class is associated with each 2-cocycle.

The results apply to many twisted crossed products of k-graph algebras.

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.