Abstract

We describe the primitive ideal space of the $C^{\ast}$algebra of a
rowfinite $k$graph with no sources when every ideal is gauge invariant. We
characterize which spectral spaces can occur, and compute the primitive ideal
space of two examples. In order to do this we prove some new results on
aperiodicity. Our computations indicate that when every ideal is gauge
invariant, the primitive ideal space only depends on the 1skeleton of the
$k$graph in question.