Related papers: Double Fell bundles over discrete double groupoids…
We extend the spectral theory of commutative C*-categories to the non full-case, introducing a suitable notion of spectral spaceoid provinding a duality between a category of "non-trivial" *-functors of non-full commutative C*-categories…
Given a saturated Fell bundle A over an inverse semigroup S which is semi-abelian in the sense that the fibers over the idempotents of S are commutative, we construct a twisted etale groupoid L such that A can be recovered from L in a…
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…
Enveloping $C^*$-algebras for some finitely generated $*$-algebras are considered. It is shown that all of the considered algebras are identically defined by their dual spaces. The description in terms of matrix-functions is given. Keywords…
Gelfand duality between unital commutative C*-algebras and Compact Hausdorff spaces is extended to all unital C*-algebras, where the dual objects are what we call compact Hausdorff quantum spaces. We apply this result to obtain, a…
We unify the classic Dauns-Hofmann representation with Kumjian and Renault's Weyl groupoid representation. More precisely, we use ultrafilters to represent C*-algebras with some additional structure on Fell bundles over locally compact…
This work provides a generalization of the Gelfand duality to the context of noncommutative locally $C^*$ algebras. Using a reformulation of a theorem proven by Dauns and Hofmann in the 60's we show that every locally $C^*$ algebra can be…
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 Fell bundles on groupoids from the viewpoint of quantale theory. Given any saturated upper semicontinuous Fell bundle $\pi:E\to G$ on an \'etale groupoid $G$ with $G_0$ locally compact Hausdorff, equipped with a suitable completion…
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…
C*-algebras form rather general and rich mathematical structures that can be studied with different morphisms (preserving multiplication, or not), and with different properties (commutative, or not). These various options can be used to…
We study the notion of duality in the context of graded manifolds. For graded bundles, somehow like in the case of Gelfand representation and the duality: points vs. functions, we obtain natural dual objects which belongs to a different…
Gelfand duality is a fundamental result that justifies thinking of general unital $C^*$-algebras as noncommutative versions of compact Hausdorff spaces. Inspired by this perspective, we investigate what noncommutative measurable spaces…
The notion of textile system was introduced by M. Nasu in order to analyze endomorphisms and automorphisms of topological Markov shifts. A textile system is given by two finite directed graphs $G$ and $H$ and two morphisms $p,q:G\to H$,…
We construct a noncommutative geometry with generalised `tangent bundle' from Fell bundle $C^*$-categories ($E$) beginning by replacing pair groupoid objects (points) with objects in $E$. This provides a categorification of a certain class…
We generalise the Dixmier-Douady classification of continuous-trace C*-algebras to Fell algebras. To do so, we show that C*-diagonals in Fell algebras are precisely abelian subalgebras with the extension property, and use this to prove that…
We explicitly construct the C*-algebras arising in the formalism of Topological T-duality due to Mathai and Rosenberg from string-theoretic data in several key examples. We construct a continuous-trace algebra with an action of ${\mathbb…
In this paper we study the nuclearity and weak containment property of reduced cross-sectional C*-algebras of Fell bundles over inverse semigroups. In order to develop the theory, we first prove an analogue of Fell's absorption trick in the…
We define the Zappa-Sz\'{e}p product of a Fell bundle by a groupoid, which turns out to be a Fell bundle over the Zappa-Sz\'{e}p product of the underlying groupoids. Under certain assumptions, every Fell bundle over the Zappa-Sz\'{e}p…
Following Crane's suggestion that categorification should be of fundamental importance in quantising gravity, we show that finite dimensional even $S^o$-real spectral triples over $\bbc$ are already nothing more than full C*-categories…