Related papers: Cross-sectional C*-algebras associated to subgroup…

Let $A$ and $B$ be $C^*$-algebras with $A\subseteq M(B)$. Exploiting the duality between sober spaces and spatial locales, and the adjunction between restriction and induction for ideals in $A$ and $B$, we identify conditions that allow to…

For a completely Hausdorff quasi-topological group $G$, we construct a universal pro-$C^*$-algebra $C(E^+G)$ as the non-commutative geometer's analogue of the total space $EG$ of the classifying principal $G$-bundle $EG\to BG$. The…

We extend the Gelfand-Naimark duality of commutative C*-algebras, "A COMMUTATIVE C*-ALGEBRA -- A LOCALLY COMPACT HAUSDORFF SPACE" to "A C*-ALGEBRA--A QUOTIENT OF A LOCALLY COMPACT HAUSDORFF SPACE". Thus, a C*-algebra is isomorphic to the…

Let E be a second-countable, locally compact, Hausdorff groupoid equipped with an action of T such that G:=E/T is a principal groupoid with Haar system \lambda. The twisted groupoid C*-algebra C*(E;G,\lambda) is a quotient of the C*-algebra…

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…

Let $\gamma = (\gamma_1,...,\gamma_N)$, $N \geq 2$, be a system of proper contractions on a complete metric space. Then there exists a unique self-similar non-empty compact subset $K$. We consider the union ${\mathcal G} = \cup_{i=1}^N…

We generalize Renault's notion of measurewise amenability to actions of second countable, Hausdorff, \'etale groupoids on separable $C^*$-algebras and show that measurewise amenability characterizes nuclearity of the crossed product…

We define and study large and stably large subalgebras of simple unital C*-algebras. The basic example is the orbit breaking subalgebra of a crossed product by Z, as follows. Let X be an infinite compact metric space, let h be a minimal…

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.…

The question of which separable C*-algebras have abelian central sequence algebras was raised and studied by Phillips ([Ph88]) and Ando-Kirchberg ([AK14]). In this paper we give a complete answer to their question: A separable C*-algebra…

We prove that if a connected and simply connected Lie group $G$ admits connected closed normal subgroups $G_1\subseteq G_2\subseteq \cdots \subseteq G_m=G$ with $\dim G_j=j$ for $j=1,\dots,m$, then its group $C^*$-algebra has closed…

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…

We show how to extend a classic Morita Equivalence Result of Green's to the \cs-algebras of Fell bundles over transitive groupoids. Specifically, we show that if $p:\B\to G$ is a saturated Fell bundle over a transitive groupoid $G$ with…

The following topics are presented in these notes: Elements of Banach algebras, Banach algebras of the form $L^1(G)$, where $G$ is a locally compact group, spectrum of elements of Banach algebras, the spectral theory of compact operators on…

We develop a framework suitable for obtaining simplicity criteria for reduced $C^*$-algebras of Hausdorff etale groupoids. This is based on the study of certain non-degenerate $C^*$-subalgebras (in the case of groupoids, the $C^*$-algebra…

We prove a spectral theorem for bimodules in the context of graph C*-algebras. A bimodule over a suitable abelian algebra is determined by its spectrum (i.e., its groupoid partial order) iff it is generated by the Cuntz-Krieger partial…

We show that if $G$ is a second countable locally compact Hausdorff \'etale groupoid carrying a suitable cocycle $c:G\to\mathbb{Z}$, then the reduced $C^*$-algebra of $G$ can be realised naturally as the Cuntz-Pimsner algebra of a…

We extend our previous results on generalized Dixmier-Douady theory to graded $C^*$-algebras, as means for explicit computations of the invariants arising for bundles of ungraded $C^*$-algebras. For a strongly self-absorbing $C^*$-algebra…

We show that there is a functor from the category of positive admissible ternary rings to the category of $*$-algebras, which induces an isomorphism of partially ordered sets between the families of $C^*$-norms on the ternary ring and its…

We consider fiberwise singly generated Fell-bundles over etale groupoids. Given a continuous real-valued 1-cocycle on the groupoid, there is a natural dynamics on the cross-sectional algebra of the Fell bundle. We study the…