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We introduce a subclass of recursive subhomogeneous algebras, in which each of the pullback maps is diagonal in a suitable sense. We define the notion of a diagonal map between two such algebras and show that every simple inductive limit of these algebras with diagonal bonding maps has stable rank one. As an application, we prove that for any infinite compact metric space $T$ and minimal homeomorphism $h\colon T\to T$, the associated dynamical crossed product $\mathrm{C^*}(\mathbb{Z},T,h)$ has stable rank one. This affirms a conjecture of Archey, Niu, and Phillips. We also show that the Toms-Winter Conjecture holds for such crossed products., Comment: Final Journal Submission. To Appear in the Muenster Journal of Mathematics

We generalize Condition (K) from directed graphs to Boolean dynamical systems and show that a locally finite Boolean dynamical system $(\mathcal{B},\mathcal{L},\theta)$ with countable $\mathcal{B}$ and $\mathcal{L}$ satisfies Condition (K) if and only if every ideal of its $C^*$-algebra is gauge-invariant, if and only if its $C^*$-algebra has the (weak) ideal property, and if and only if its $C^*$-algebra has topological dimension zero. As a corollary we prove that if the $C^*$-algebra of a locally finite Boolean dynamical system with $\mathcal{B}$ and $\mathcal{L}$ are countable either has real rank zero or is purely infinite, then $(\mathcal{B}, \mathcal{L}, \theta)$ satisfies Condition (K). We also generalize the notion of maximal tails from directed graph to Boolean dynamical systems and use this to give a complete description of the primitive ideal space of the $C^*$-algebra of a locally finite Boolean dynamical system that satisfies Condition (K) and has countable $\mathcal{B}$ and $\mathcal{L}$., Comment: 25 pages. Version 2 is a minor update of version 1 and is the version that will be published in J. Aust. Math. Soc

We define and study large and stably large subalgebras of simple unital C*-algebras. The basic example is the orbit breaking subalgebra of a crossed product by Z, as follows. Let X be an infinite compact metric space, let h be a minimal homeomorphism of X, and let Y be a closed subset of X. Let u be the standard unitary in C* (Z, X, h). The Y-orbit breaking subalgebra is the subalgebra of C* (Z, X, h) generated by C (X) and all elements f u for f in C (X) such that f vanishes on Y. If intersects each orbit of h at most once, then the Y-orbit breaking subalgebra is large in C* (Z, X, h). Large subalgebras obtained via generalizations of this construction have appeared in a number of places, and we unify their theory in this paper. We prove the following results for an infinite dimensional simple unital C*-algebra A and a stably large subalgebra B of A: B is simple and infinite dimensional. If B is stably finite then so is A, and if B is purely infinite then so is A. The restriction maps from the tracial states of A to the tracial states of B and from the normalized 2-quasitraces on A to the normalized 2-quasitraces on B are bijective. When A is stably finite, the inclusion of B in A induces an isomorphism on the semigroups that remain after deleting from the Cuntz semigroups of A and B all the classes of nonzero projections. B and A have the same radius of comparison., Comment: 54 pages; AMSLaTeX

We define proper, free and commuting partial actions on upper semicontinuous bundles of $C^*-$algebras. With such, we construct the $C^*-$algebra induced by a partial action and a partial actions on that algebra. Using those action we give a generalization, to partial actions, of Raeburn's Symmetric Imprimitivity Theorem.

The C*-algebra of a skew-product topological graph is a crossed product of the C*-algebra of the base topological graph by a coaction., Comment: minor corrections