Simplicity of C-algebras Associated to Row-finite Locally Convex Higher-rank Graphs

In previous work, the authors showed that the C∗-algebra C∗(Λ) of a rowfinite higher-rank graph Λ with no sources is simple if and only if Λ is both cofinal and aperiodic. In this paper, we generalise this result to row-finite higher-rank graphs which are locally convex (but may contain sources). Our main tool is Farthing’s “removing sources” construction which embeds a row-finite locally convex higher-rank graph in a row-finite higher-rank graph with no sources in such a way that the associated C∗algebras are Morita equivalent.