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 -algebras associated to strongly connected row-finite -graphs . We begin by giving an alternative characterization of the -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 construct a faithful separable representation for any row-finite source-free -graph.
Keywords
Cite
@article{arxiv.1803.08779,
title = {Representations of higher-rank graph $C^*$-algebras associated to $\Lambda$-semibranching function systems},
author = {Carla Farsi and Elizabeth Gillaspy and Palle E. T. Jorgensen and Sooran Kang and Judith Packer},
journal= {arXiv preprint arXiv:1803.08779},
year = {2018}
}
Comments
This paper constitutes a partial replacement of arXiv:1709.00592; the latter will not be submitted for publication