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.

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, Professor Mike
• 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