Related papers: Groupoid Actions on Fractafolds

Consider the Deaconu-Renault groupoid of an action of a finitely generated free abelian monoid by local homeomorphisms of a locally compact Hausdorff space. We catalogue the primitive ideals of the associated groupoid C*-algebra. For a…

We consider Deaconu--Renault groupoids associated to actions of finite-rank free abelian monoids by local homeomorphisms of locally compact Hausdorff spaces. We study simplicity of the twisted C*-algebra of such a groupoid determined by a…

We introduce the notion of continuous twisted partial actions of a locally compact group on a C*-algebra. With such, we construct an associated C*-algebraic bundle called the semidirect product bundle. Our main theorem shows that, given any…

Given an action of a groupoid by isomorphisms on a Fell bundle (over another groupoid), we form a semidirect-product Fell bundle, and prove that its $C^{*}$-algebra is isomorphic to a crossed product.

We give a length one projective resolution of the trivial module for the groupoid of a semi-saturated partial action (in the sense of Exel) of a free group on a compact Hausdorff and totally disconnected space. As a consequence we obtain an…

Let $C^*$-algebra that is acted upon by a compact abelian group. We show that if the fixed-point algebra of the action contains a Cartan subalgebra $D$ satisfying an appropriate regularity condition, then $A$ is the reduced $C^*$-algebra of…

We define a groupoid from a labelled space and show that it is isomorphic to the tight groupoid arising from an inverse semigroup associated with the labelled space. We then define a local homeomorphism on the tight spectrum that is a…

Let G be a locally compact Abelian group. Following Ruy Exel, we view Fell bundles over the Pontrjagin dual of G as continuous spectral decompositions of G-actions on C*-algebras. We classify such spectral decompositions using certain dense…

Groupoid actions on C*-bundles and inverse semigroup actions on C*-algebras are closely related when the groupoid is r-discrete.

The second author showed how Katsura's construction of the C*-algebra of a topological graph E may be twisted by a Hermitian line bundle L over the edge space E. The correspondence defining the algebra is obtained as the completion of the…

We study the C*-algebras of Fell bundles. In particular, we prove the analogue of Renault's disintegration theorem for groupoids. As in the groupoid case, this result is the key step in proving a deep equivalence theorem for the C*-algebras…

We study Deaconu-Renault groupoids corresponding to surjective local homeomorphisms on locally compact, Hausdorff, second countable, totally disconnected spaces, and we characterise when the C*-algebras of these groupoids are AF embeddable.…

We introduce a notion of the Rapid Decay Property (RDP) for Fell bundles over locally compact Hausdorff \'etale groupoids, extending earlier rapid decay theories for \'etale groupoids and twists. Our approach yields analytic control on…

We provide a framework for studying concrete C*-algebras associated with algebraic actions of semigroups: Given such an action, we construct an inverse semigroup, and we introduce conditions for algebraic actions that characterize…

We introduce and study actions of Fell bundles over discrete groups on Hilbert bundles. Many examples of such actions are presented. We discuss the connection with positive definite bundle maps between Fell bundles, culminating in the…

Given a normal subgroup bundle $\mathcal A$ of the isotropy bundle of a groupoid $\Sigma$, we obtain a twisted action of the quotient groupoid $\Sigma/\mathcal A$ on the bundle of group $C^*$-algebras determined by $\mathcal A$ whose…

We study the $C^*$-algebras associated to upper-semicontinuous Fell bundles over second-countable Hausdorff groupoids. Based on ideas going back to the Packer--Raeburn "Stabilization Trick," we construct from each such bundle a groupoid…

We define possibly unsaturated, upper semicontinuous Fell bundles over Hausdorff, locally compact groupoids and establish a universal property for representations of their full section C*-algebras on Hilbert modules over arbitrary…

We describe the envelope C*-algebra associated to a partial action of a countable discrete group on a locally compact space as a groupoid C*-algebra (more precisely as a C*-algebra from an equivalence relation) and we use our approach to…

In this paper we study deformations of $C^*$-algebras that are given as cross-sectional $C^*$-algebras of Fell bundles over locally compact groups $G$. Our deformation comes from a direct deformation of the Fell bundles via certain…