Related papers: The ideal intersection property for essential grou…

A $C^*$-algebra $A$ is said to have the ideal property if each closed two-sided ideal of $A$ is generated by the projections inside the ideal, as a closed two sided ideal. $C^*$-algebras with the ideal property are generalization and…

It is proved that for every ICC group which is embeddable into a hyperbolic group, the reduced group C*-algebra is realized as the intersection of a decreasing sequence of isomorphs of the Cuntz algebra O_2. The proof is based on the study…

To a large class of graphs of groups we associate a C*-algebra universal for generators and relations. We show that this C*-algebra is stably isomorphic to the crossed product induced from the action of the fundamental group of the graph of…

Exotic group $C^*$-algebras are $C^*$-algebras that lie between the universal and the reduced group $C^*$-algebra of a locally compact group. We consider simple Lie groups $G$ with real rank one and investigate their exotic group…

For an action of a finite group on a C*-algebra, we present some conditions under which properties of the C*-algebra pass to the crossed product or the fixed point algebra. We mostly consider the ideal property, the projection property,…

Our purpose is to study in the setting of locally compact groupoids the analogues of the well-known equivalent definitions of exactness for discrete groups. Our best results are obtained for a class of \'etale groupoids that we call inner…

We prove the Effros-Hahn conjecture for groupoid algebras with coefficients in a sheaf, obtaining as a consequence a description of the ideals in skew inverse semigroup rings. We also use the description of the ideals to characterize when…

The study of different types of ideals in non self-adjoint operator algebras has been a topic of recent research. This study focuses on principal ideals in subalgebras of groupoid C*-algebras. An ideal is said to be principal if it is…

We consider group actions of topological groups on C*-algebras of the types which occur in many physics models. These are singular actions in the sense that they need not be strongly continuous, or the group need not be locally compact. We…

We show how to construct a graded locally compact Hausdorff \'etale groupoid from a C*-algebra carrying a coaction of a discrete group, together with a suitable abelian subalgebra. We call this groupoid the extended Weyl groupoid. When the…

Suppose G is a second countable, locally compact, Hausdorff, principal groupoid with a fixed left Haar system. We define a notion of integrability for groupoids, and show G is integrable if and only if the groupoid C*-algebra C*(G) has…

Let $G$ be a locally compact abelian Hausdorff topological group which is non-compact and whose Pontryagin dual $\Gamma$ is partially ordered. Let $\Gamma^{+}\subset\Gamma$ be the semigroup of positive elements in $\Gamma$. The Hardy space…

We study simplicity and pure infiniteness criteria for C*-algebras associated to inverse semigroup actions by Hilbert bimodules and to Fell bundles over etale not necessarily Hausdorff groupoids. Inspired by recent work of Exel and Pitts,…

Let $\alpha : \Gamma \curvearrowright A$ be an action of a discrete group $\Gamma$ on a unital C*-algebra $A$ by *-automorphisms and let $A \rtimes_{\alpha,\lambda} \Gamma$ denote the corresponding reduced crossed product C*-algebra.…

We study the question whether the representations defined by a dense subset of the unit space of a locally compact \'etale groupoid are enough to determine the reduced norm on the groupoid C$^*$-algebra. We present sufficient conditions for…

We consider the ideal structure of reduced crossed products over discrete groups. First, we completely characterize primality for reduced crossed products. Second, we characterize the ideal intersection property for reduced crossed products…

This paper studies injective envelopes of groupoid dynamical systems and the corresponding boundaries. Analogue to the group case, we associate a bundle of compact Hausdorff spaces to any (discrete) groupoid (the Hamana boundary of the…

For an \'{e}tale groupoid, we define a pairing between the Crainic-Moerdijk groupoid homology and the simplex of invariant Borel probability measures on the base space. The main novelty here is that the groupoid need not have totally…

A discrete group is said to be C*-simple if its reduced C*-algebra is simple, and is said to have the unique trace property if its reduced C*-algebra has a unique tracial state. A dynamical characterization of C*-simplicity was recently…

Let G be a locally compact, Hausdorff groupoid in which s is a local homeomorphism and the unit space is totally disconnected. Assume there is a continuous cocycle c from G into a discrete group $\Gamma$. We show that the collection A(G) of…