Twisted -algebras associated to finitely aligned higher-rank graphs

  • Aidan Sims

  • Benjamin Whitehead

  • Michael F. Whittaker

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

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Aidan Sims, Benjamin Whitehead, Michael F. Whittaker, Twisted -algebras associated to finitely aligned higher-rank graphs. Doc. Math. 19 (2014), pp. 831–866

DOI 10.4171/DM/466