Coverings of skew-products and crossed products by coactions

Consider a projective limit G of finite groups G_n. Fix a compatible family \delta^n of coactions of the G_n on a C*-algebra A. From this data we obtain a coaction \delta of G on A. We show that the coaction crossed product of A by \delta is isomorphic to a direct limit of the coaction crossed products of A by the \delta^n. If A = C*(\Lambda) for some k-graph \Lambda, and if the coactions \delta^n correspond to skew-products of \Lambda, then we can say more. We prove that the coaction crossed-product of C*(\Lambda) by \delta may be realised as a full corner of the C*-algebra of a (k+1)-graph. We then explore connections with Yeend's topological higher-rank graphs and their C*-algebras.Comment: 19 pages, laTeX. v2: Minor modifications to version 1. This version to appear in the Journal of the Australian Mathematical Society v3: some potentially confusing typos corrected in the proof of Theorem~3.1, as well as a few others. References update

A Comparative Study of Basic Concerns of Eighth and Tenth Grade Students

The purpose of this study was to compare the basic concerns of a group of early adolescent students with those of a mid-adolescent group

The C∗C^*-algebras of finitely aligned higher-rank graphs

We generalise the theory of Cuntz-Krieger families and graph algebras to the class of finitely aligned $k$-graphs. This class contains in particular all row-finite $k$-graphs. The Cuntz-Krieger relations for non-row-finite $k$-graphs look significantly different from the usual ones, and this substantially complicates the analysis of the graph algebra. We prove a gauge-invariant uniqueness theorem and a Cuntz-Krieger uniqueness theorem for the $C^*$-algebras of finitely aligned $k$-graphs.Comment: 27 page

Uniqueness Theorems For Topological Higher-rank Graph C*-algebras

We consider the boundary-path groupoids of topological higher-rank graphs. We show that all such groupoids are topologically amenable. We deduce that the $C^*$-algebras of topological higher-rank graphs are nuclear and prove versions of the gauge-invariant uniqueness theorem and the Cuntz-Krieger uniqueness theorem. We then provide a necessary and sufficient condition for simplicity of a topological higher-rank graph $C^*$-algebra, and a condition under which it is also purely infinite