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The uncovering of new structure on the Cuntz semigroup of a C*-algebra of stable rank one leads to several applications: We answer affirmatively, for the class of stable rank one C*-algebras, a conjecture by Blackadar and Handelman on…

Given an ample action of an inverse semigroup on a locally compact and Hausdorff topological space, we study the ideal structure of the crossed product algebra associated with it. By developing a theory of induced ideals, we manage to prove…

Suppose $\mathcal{G}$ is a second-countable locally compact Hausdorff \'{e}tale groupoid, $G$ is a discrete group containing a unital subsemigroup $P$, and $c:\mathcal{G}\rightarrow G$ is a continuous cocycle. We derive conditions on the…

We show that the property of being rationally $K$-stable passes from the fibers of a continuous $C(X)$-algebra to the ambient algebra, under the assumption that the underlying space $X$ is compact, metrizable, and of finite covering…

We prove a version of the result in the title that makes use of maximal coactions in the context of discrete groups. Earlier Gauge-Invariant Uniqueness theorems for $C^*$-algebras associated to $P$-graphs and similar $C^*$-algebras…

In this paper, we study a family of $C^*$-subalgebras defined by fixed points of generalized gauge actions of a Cuntz-Krieger algebra, by introducing a family of \'etale groupoids whose associated $C^*$-algebras are these $C^*$-subalgebras.…

We introduce a class of locally compact Hausdorff groupoids and show how to associate C*-algebras to them in a way which generalizes the reduced C*-algebra of an 'etale groupoid. Focusing on criteria for simplicity and existence of Cartan…

Let $1 \in A \subset B$ be an inclusion of C*-algebras of C*-index-finite type with depth 2. We try to compute topological stable rank of $B$ ($= \tsr(B)$) when $A$ has topological stable rank one. We show that $\tsr(B) \leq 2$ when $A$ is…

We define continuous C*-algebras over a topological space X and establish some basic results. If X is a locally compact Hausdorff space, continuous C*-algebras over X are equivalent to ordinary continuous C_0(X)-algebras. The main purpose…

We investigate recent uniqueness theorems for reduced $C^*$-algebras of Hausdorff \'{e}tale groupoids in the context of inverse semigroups. In many cases the distinguished subalgebra is closely related to the structure of the inverse…

Given a field $K$ and an ample (not necessarily Hausdorff) groupoid $G$, we define the concept of a line bundle over $G$ inspired by the well known concept from the theory of C*-algebras. If $E$ is such a line bundle, we construct the…

This paper investigates the $\mathrm{K}$-theory of twisted groupoid $\mathrm{C}^*$-algebras. It is shown that a homotopy of twists on an ample groupoid satisfying the Baum-Connes conjecture with coefficients gives rise to an isomorphism…

Let G be a compact, simple and simply connected Lie group and $\A$ be an equivariant Dixmier-Douady bundle over G. For any fixed level k, we can define a G-C*-algebra $C_{\A^{k+h}}(G)$ as all the continuous sections of the tensor power…

A duality is discussed for Lie group bundles vs. certain tensor categories with non-simple identity, in the setting of Nistor-Troitsky gauge-equivariant K-theory. As an application, we study C*-algebra bundles with fibre a fixed-point…

We prove that separable, simple, unital, non-elementary, stably finite C*-algebras that have stable rank one, and that have locally finite nuclear dimension in a tracial sense, have uniform property $\Gamma$. In particular, Villadsen…

Given a pseudo-free self-similar action of a countable group $G$ on a countable directed graph $E$ with amenable stabilizers of the vertices, we identify the exact conditions under which these stabilizers do not contribute to the ideal…

Given an ample groupoid, we construct a spectral sequence with groupoid homology with integer coefficients on the second sheet, converging to the K-groups of the (reduced) groupoid C*-algebra, provided the groupoid has torsion-free…

In recent work, Cuntz, Deninger and Laca have studied the Toeplitz type C*-algebra associated to the affine monoid of algebraic integers in a number field, under a time evolution determined by the absolute norm. The KMS equilibrium states…

We introduce the notion of continuous orbit equivalence for partial dynamical systems, and give an equivalent characterization in terms of Cartan-isomorphisms for partial C*-crossed products. Both graph C*-algebras and semigroup C*-algebras…

We describe representations of groupoid C*-algebras on Hilbert modules over arbitrary C*-algebras by a universal property. For Hilbert space representations, our universal property is equivalent to Renault's Integration-Disintegration…