Twisted C*-algebras associated to finitely aligned higher-rank graphs
Abstract
We introduce twisted relative Cuntz-Krieger algebras associated to finitely aligned higher-rank graphs and give a comprehensive treatment of their fundamental structural properties. We establish versions of the usual uniqueness theorems and the classification of gauge-invariant ideals. We show that all twisted relative Cuntz-Krieger algebras associated to finitely aligned higher-rank graphs are nuclear and satisfy the UCT, and that for twists that lift to real-valued cocycles, the K-theory of a twisted relative Cuntz-Krieger algebra is independent of the twist. In the final section, we identify a sufficient condition for simplicity of twisted Cuntz-Krieger algebras associated to higher-rank graphs which are not aperiodic. Our results indicate that this question is significantly more complicated than in the untwisted setting.
Keywords
Cite
@article{arxiv.1310.7656,
title = {Twisted C*-algebras associated to finitely aligned higher-rank graphs},
author = {Aidan Sims and Benjamin Whitehead and Michael F. Whittaker},
journal= {arXiv preprint arXiv:1310.7656},
year = {2014}
}
Comments
Version 2: This paper has now appeared in Documenta Mathematica. This version on arXiv exactly matches the pagination and format of the published version. Original published version available from http://www.math.uni-bielefeld.de/documenta/vol-19/28.html