Related papers: Graphs of $C^*$-correspondences and Fell bundles

A cosystem consists of a possibly nonselfadoint operator algebra equipped with a coaction by a discrete group. We introduce the concept of C*-envelope for a cosystem; roughly speaking, this is the smallest C*-algebraic cosystem that…

Given a compact space X and two commuting continuous open surjective maps sigma_1, sigma_2 : X --> X, we construct certain C*-algebras that reflect the dynamics of the N^2-action. When the maps sigma_1, sigma_2 are local homeomorphisms,…

We consider two saturated Fell bundles over a countable discrete group, whose unit fibers are $\sigma$-unital $C^*$-algebras. Then by taking the reduced cross-sectional $C^*$-algebras, we get two inclusions of $C^*$-algebras. We suppose…

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 define a categorical framework in which we build a systematic construction that provides generic invariants for C*-algebras. The benefit is significant as we show that any invariant arising this way automatically enjoys nice properties…

Topological quivers generalize the notion of directed graphs in which the sets of vertices and edges are locally compact (second countable) Hausdorff spaces. Associated to a topological quiver $Q$ is a $C^*$-correspondence, and in turn, a…

We define the categorical cohomology of a k-graph \Lambda\ and show that the first three terms in this cohomology are isomorphic to the corresponding terms in the cohomology defined in our previous paper. This leads to an alternative…

Examples of Fell algebras with compact spectrum and trivial Dixmier-Douady invariant are constructed to illustrate differences with the case of continuous trace $C^*$-algebras. At the level of the spectrum, this translates to only assuming…

We introduce a natural concept of positive definiteness for bundle maps between Fell bundles over (possibly different) discrete groups and describe several examples. Such maps induce completely positive maps between the associated full…

We provide a Cuntz-Pimsner model for graph of groups $C^*$-algebras. This allows us to compute the $K$-theory of a range of examples and show that graph of groups $C^*$-algebras can be realised as Exel-Pardo algebras. We also make a…

We show that the C*-algebra of a row-finite source-free k-graph is Rieffel-Morita equivalent to a crossed product of an AF algebra by the fundamental group of the k-graph. When the k-graph embeds in its fundamental groupoid, this AF algebra…

From a planar algebra, we give a functorial construction to produce numerous associated $C^*$-algebras. Our main construction is a Hilbert $C^*$-bimodule with a canonical real subspace which produces Pimsner-Toeplitz, Cuntz-Pimsner, and…

A method for deforming C*-algebras is introduced, which applies to C*-algebras that can be described as the cross-sectional C*-algebra of a Fell bundle. Several well known examples of non-commutative algebras, usually obtained by deforming…

In this paper we construct the notions of double Fell bundle and double C*-category for possible future use as tools to describe noncommutative spaces, in particular in finite dimensions. We identify the algebra of sections of a double Fell…

We produce a complete descrption of the lattice of gauge-invariant ideals in $C^*(\Lambda)$ for a finitely aligned $k$-graph $\Lambda$. We provide a condition on $\Lambda$ under which every ideal is gauge-invariant. We give conditions on…

We introduce a notion of $\lambda$-graph bisystem. It consists of a pair $({\frak L}^-, {\frak L}^+)$ of two labeled Bratteli diagrams ${\frak L}^-, {\frak L}^+$ over alphabets $\Sigma^-, \Sigma^+$, respectively, and satisfy certain…

Given a full right-Hilbert C*-module $\mathbf{X}$ over a C*-algebra $A$, the set $\mathbb{K}_{A}(\mathbf{X})$ of $A$-compact operators on $\mathbf{X}$ is the (up to isomorphism) unique C*-algebra that is strongly Morita equivalent to the…

In this paper we study Cuntz--Pimsner algebras associated to $\mathrm{C}^*$-correspondences over commutative $\mathrm{C}^*$-algebras from the point of view of the $\mathrm{C}^*$-algebra classification programme. We show that when the…

We introduce the notion of groupoid pre-equivalences and prove that they give rise to groupoid equivalences by taking certain quotients. Then, given an equivalence of Fell bundles $\mathscr{B}$ and $\mathscr{C}$ and another equivalence…

We show that the passage from a $C^\ast$-correspondence to its Cuntz-Pimsner $C^\ast$-algebra gives a functor on a category of $C^\ast$-correspondences with appropriately defined morphisms. Applications involving topological graph…