Geodesic
Twisted $C^*$-algebras associated to finitely aligned higher-rank graphs
Documenta mathematica, Tome 19 (2014), pp. 831-866.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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.
Classification : 46L05
Keywords: C^*-algebra, graph algebra, Cuntz-Krieger algebra 
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     title = {Twisted $C^*$-algebras associated to finitely aligned higher-rank graphs},
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     url = {http://geodesic.mathdoc.fr/item/DOCMA_2014__19__a17/}
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Sims, Aidan; Whitehead, Benjamin; Whittaker, Michael F. Twisted $C^*$-algebras associated to finitely aligned higher-rank graphs. Documenta mathematica, Tome 19 (2014), pp. 831-866. http://geodesic.mathdoc.fr/item/DOCMA_2014__19__a17/