Geodesic
Twisted $C^*$-algebras associated to finitely aligned higher-rank graphs
Documenta mathematica, Tome 19 (2014), pp. 831-866
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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.
DOI : 10.4171/dm/466
Classification : 46L05
Mots-clés : graph algebra, C\^\*-algebra, Cuntz-Krieger algebra 
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     author = {Benjamin Whitehead and Aidan Sims and Michael F. Whittaker},
     title = {Twisted $C^*$-algebras associated to finitely aligned higher-rank graphs},
     journal = {Documenta mathematica},
     pages = {831--866},
     year = {2014},
     volume = {19},
     doi = {10.4171/dm/466},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/466/}
}
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Benjamin Whitehead; Aidan Sims; Michael F. Whittaker. Twisted $C^*$-algebras associated to finitely aligned higher-rank graphs. Documenta mathematica, Tome 19 (2014), pp. 831-866. doi: 10.4171/dm/466

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