Related papers: Quantales and Fell bundles

To every Fell bundle $\mathscr C$ over a locally compact group ${\sf G}$ one associates a Banach $^*$-algebra $L^1({\sf G}\,\vert\,\mathscr C)$. We prove that it is symmetric whenever ${\sf G}$ with the discrete topology is rigidly…

We consider a locally compact Hausdorff groupoid $G$ which is graded over a discrete group. Then the fibre over the identity is an open and closed subgroupoid $G_e$. We show that both the full and reduced C*-algebras of this subgroupoid…

We study the projections of an arbitrary stably Gelfand quantale $Q$ and show that each projection determines a pseudogroup $S\subset Q$ (and a corresponding localic \'etale groupoid $G$) together with a map of involutive quantales…

In this paper, we show that if E is a Fell bundle over an amenable \'etale locally compact Hausdorff groupoid such that every fiber on the unit space is nuclear, then $C?^*r(E)$ is also nuclear. In order to show this result, we introduce…

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…

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…

We give a notion of equivalence for Fell bundles over groups, not necessarily saturated nor separable, and show that equivalent Fell bundles have Morita-Rieffel equivalent cross-sectional $C^*$-algebras. Our notion is originated in the…

For any Lie groupoid $G$, the vector bundle $g^*$ dual to the associated Lie algebroid $g$ is canonically a Poisson manifold. The (reduced) C*-algebra of $G$ (as defined by A. Connes) is shown to be a strict quantization (in the sense of M.…

Let $P$ be a submonoid of a group $G$ and let $\mathcal{E}=(\mathcal{E}_p)_{p\in P}$ be a product system over $P$ with coefficient C*-algebra $A$. We show that the following C*-algebras are canonically isomorphic: the C*-envelope of the…

We investigate amenability for $W^*$-Fell bundles over a discrete group $G$, with a focus on its characterization via approximation properties and conditional expectations. Building on the notion of $W^*$-amenability, we construct an…

Let $p\colon \mathcal{A} \to G$ be a saturated Fell bundle over a locally compact, Hausdorff, second countable, {\'e}tale groupoid~$G$, and let $\mathrm{C}^*(G;\mathcal{A})$ denote its full $\mathrm{C}^*$-algebra. We prove an…

Given a C*-algebra B which is graded over a discrete group G we consider ideals of B which are invariant under the projections onto each of the grading subspaces. If G is exact and the standard conditional expectation of B is faithful we…

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 study two classes of operator algebras associated with a unital subsemigroup $P$ of a discrete group $G$: one related to universal structures, and one related to co-universal structures. First we provide connections between universal…

Let $X$ be a complex hypersurface in a $\mathbf{P}^n$-bundle over a curve $C$. Let $C'\to C$ be a Galois cover with group $G$. In this paper we describe the $\mathbf{C}[G]$-structure of $H^{p,q}(X\times_C C')$ provided that $X\times_C C'$…

We show that if E is an equivalence of upper semicontinuous Fell bundles B and C over groupoids, then there is a linking bundle L(E) over the linking groupoid L such that the full cross-sectional algebra of L(E) contains those of B and C as…

We define the notion of a $\Lambda$-system of $C^*$-correspondences associated to a higher-rank graph $\Lambda$. Roughly speaking, such a system assigns to each vertex of $\Lambda$ a $C^*$-algebra, and to each path in $\Lambda$ a…

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 prove that if A and B are Fell bundles over the locally compact groups G and H respectively, then the minimal (maximal) tensor product of the C*-algebra of kernels of A with the C*-algebra of kernels of B agrees with the C*-algebra of…

Let G be a simple and simply connected complex linear algebraic group. In this paper, we discuss the generalization of the parabolic construction of holomorphic principal G-bundles over a smooth elliptic curve to the case of a singular…