• DOI:10.4171/dm/466
• Corpus ID: 9315836

Twisted $C^*$-algebras associated to finitely aligned higher-rank graphs

@article{Sims2013TwistedA,
  title={Twisted \$C^*\$-algebras associated to finitely aligned higher-rank graphs},
  author={Aidan Sims and Benjamin Whitehead and Michael F. Whittaker},
  journal={Documenta Mathematica},
  year={2013}
}

• A. Sims, Benjamin Whitehead, Michael F. Whittaker
• Published 29 October 2013
• Mathematics
• Documenta Mathematica

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.