Representations of higher-rank graph C*-algebras associated to Lambda-semibranching function systems

Abstract

In this paper, we discuss a method of constructing separable representations of the C*-algebras associated to strongly connected row-finite k-graphs Lambda. We begin by giving an alternative characterization of the Lambda-semibranching function systems introduced in an earlier paper, with an eye towards constructing such representations that are faithful. Our new characterization allows us to more easily check that examples satisfy certain necessary and sufficient conditions. We present a variety of new examples relying on this characterization. We then use some of these methods and a direct limit procedure to identify a faithful separable representation for any row-finite source-free k-graph. (C) 2018 Elsevier Inc. All rights reserved.