Related papers: Residually Finite Partial Actions and MF Fell Bund…

This is a book about Partial Actions and Fell Bundles with applications to C*-algebras generated by partial isometries. Here is the table of contents: 1-Introduction, 2-Partial actions, 3-Restriction and globalization, 4-Inverse semigroups,…

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 study the interplay of C*-dynamics and K-theory. Notions of chain recurrence for transformations groups (X,G) and MF actions for non-commutative C*-dynamical systems (A,G) are translated into K-theoretical language, where purely…

In the paper, we provide some examples of MF algebras by considering minimal or maximal tensor products of MF algebras and crossed products of MF algebras by finite groups or an integer group. We also present some examples of…

With each Fell bundle over a discrete group G we associate a partial action of G on the spectrum of the unit fiber. We discuss the ideal structure of the corresponding full and reduced cross-sectional C*-algebras in terms of the dynamics of…

We study the exactness of the reduced crossed product of a semigroup dynamical system and the reduced $C^{*}$-algebra of a product system. We show that for a semigroup dynamical system $(A, P,\alpha)$, under reasonable hypotheses (e.g., $P$…

We construct a weak conditional expectation from the section C*-algebra of a Fell bundle over a unital inverse semigroup to its unit fibre. We use this to define the reduced C*-algebra of the Fell bundle. We study when the reduced…

We introduce the notion of fibred action of a group bundle on a C(X)-algebra. By using such a notion, a characterization in terms of induced C*-bundles is given for C*-dynamical systems such that the relative commutant of the fixed-point…

We study a notion of residual finiteness for continuous actions of discrete groups on compact Hausdorff spaces and how it relates to the existence of norm microstates for the reduced crossed product. Our main result asserts that an action…

In this paper we give a simple proof of the maximality of dual coactions on full cross-sectional C*-algebras of Fell bundles over locally compact groups. As applications we extend certain exotic crossed-product functors in the sense of…

Let P be a left LCM semigroup, and $\alpha$ an action of $P$ by endomorphisms of a $C^{*}$-algebra $A$. We study a semigroup crossed product $C^{*}$-algebra in which the action $\alpha$ is implemented by partial isometries. This crossed…

We investigate structural properties of the reduced cross-sectional algebra $C^*_r(\mathcal{B})$ of a Fell bundle $\mathcal{B}$ over a discrete group $G$. Conditions allowing one to determine the ideal structure of $C^*_r(\mathcal{B})$ are…

We develop the notion of Rokhlin dimension for partial actions of finite groups, extending the well-established theory for global systems. The partial setting exhibits phenomena that cannot be expected for global actions, usually stemming…

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…

We define inverse semigroup actions on topological groupoids by partial equivalences. From such actions, we construct saturated Fell bundles over inverse semigroups and non-Hausdorff \'etale groupoids. We interpret these as actions on…

We define notions of semi-saturatedness and orthogonality for a Fell bundle over a quasi-lattice ordered group. We show that a compactly aligned product system of Hilbert bimodules can be naturally extended to a semi-saturated and…

We obtain a characterization in terms of dynamical systems of those r-discrete groupoids for which the groupoid C*-algebra is approximately finite-dimensional (AF). These ideas are then used to compute the K-theory for AF algebras by…

We apply the One-Sided Action Theorem from the first paper in this series to prove that Rieffel's Morita equivalence between the reduced crossed product by a proper saturated action and the generalized fixed-point algebra is a quotient of a…

We define partial product systems over N. They generalise product systems over N and Fell bundles over Z. We define Toeplitz C*-algebras and relative Cuntz-Pimsner algebras for them and show that the section C*-algebra of a Fell bundle over…

A collection of partial isometries whose range and initial projections satisfy a specified set of conditions often gives rise to a partial representation of a group. The C*-algebra generated by the partial isometries is thus a quotient of…