On twisted higher-rank graph $C^*$-algebras

Alex Kumjian, David Pask, Aidan Sims
2015 Transactions of the American Mathematical Society  
Building on recent work of Robertson and Steger, we associate a C * -algebra to a combinatorial object which may be thought of as a higher rank graph. This C * -algebra is shown to be isomorphic to that of the associated path groupoid. Various results in this paper give sufficient conditions on the higher rank graph for the associated C * -algebra to be: simple, purely infinite and AF. Results concerning the structure of crossed products by certain natural actions of discrete groups are
more » ... groups are obtained; a technique for constructing rank 2 graphs from "commuting" rank 1 graphs is given.
doi:10.1090/s0002-9947-2015-06209-6 fatcat:fk6ps7lxxnb63dqz2gsoc5zliy