Simplicity of C*-algebras associated to row-finite locally convex higher-rank graphs

TL;DR

This paper extends the simplicity characterization of C*-algebras from higher-rank graphs without sources to those with sources by using a construction that embeds locally convex graphs into source-free graphs, preserving algebraic properties.

Contribution

It generalizes the simplicity criteria for C*-algebras of higher-rank graphs to include locally convex graphs with sources, using Farthing's source-removing technique.

Findings

Established Morita equivalence between C*-algebras of locally convex graphs and source-free graphs.

Extended simplicity conditions to a broader class of higher-rank graphs.

Provided a method to analyze C*-algebras of graphs with sources through embedding techniques.

Abstract

In previous work, the authors showed that the C*-algebra C*(\Lambda) of a row-finite higher-rank graph \Lambda with no sources is simple if and only if \Lambda 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.