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

Sims, A., Whitehead, B. and Whittaker, M. (2014) Twisted C*-algebras associated to finitely aligned higher-rank graphs. Documenta Mathematica, 19, pp. 831-866.

Sims, A., Whitehead, B. and Whittaker, M. (2014) Twisted C*-algebras associated to finitely aligned higher-rank graphs. Documenta Mathematica, 19, pp. 831-866.

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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 $K$-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.

Item Type:Articles
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Whittaker, Dr Michael
Authors: Sims, A., Whitehead, B., and Whittaker, M.
Subjects:Q Science > QA Mathematics
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Documenta Mathematica
Publisher:Deutsche Mathematiker Vereinigung
ISSN:1431-0635
ISSN (Online):1431-0643
Copyright Holders:Copyright © 2014 Deutsche Mathematiker Vereinigung
First Published:First published in Documenta Mathematica 19:831-866
Publisher Policy:Reproduced in accordance with the copyright policy of the publisher

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