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

Cartan subalgebras and the UCT problem, II

We show that outer approximately represenbtable actions of a finite cyclic group on UCT Kirchberg algebras satisfy a certain quasi-freeness type property if the corresponding crossed products satisfy the UCT and absorb a suitable UHF algebra tensorially. More concretely, we prove that for such an action there exists an inverse semigroup of homogeneous partial isometries that generates the ambient C*-algebra and whose idempotent semilattice generates a Cartan subalgebra. We prove a similar result for actions of finite cyclic groups with the Rokhlin property on UCT Kirchberg algebras absorbing a suitable UHF algebra. These results rely on a new construction of Cartan subalgebras in certain inductive limits of Cartan pairs. We also provide a characterisation of the UCT problem in terms of finite order automorphisms, Cartan subalgebras and inverse semigroups of partial isometries of the Cuntz algebra $\mathcal{O}_2$. This generalizes earlier work of the authors.Comment: minor revisions; final version, accepted for publication in Math. Ann.; 26 page

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

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