Related papers: The Imprimitivity Fell Bundle

In this article, we generalize to the case of measured quantum groupoids on a finite basis some important results concerning actions of locally compact quantum groups on C*-algebras [S. Baaj, G. Skandalis and S. Vaes, 2003]. Let $\cal G$ be…

We introduce a definition of the locally trivial $G$-C*-algebra, which is a noncommutative counterpart of the total space of a locally compact Hausdorff numerable principal $G$-bundle. To obtain this generalization, we have to go beyond the…

In this exposition we highlight product systems as the semigroup analogue of Fell bundles. Motivated by Fock creation operators we extend the definition of Fowler's product systems over unital discrete left-cancellative semigroups, via both…

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…

We generalise various non-triviality conditions for group actions to Fell bundles over discrete groups and prove several implications between them. We also study sufficient criteria for the reduced section C*-algebra C_r(B) of a Fell bundle…

We study such Hilbert C*-modules over a C*-algebra $A$, that the Banach $A$-dual module carries a natural structure of Hilbert $A$-module. In this direction we prove that if $A$ is monotone complete, $M$ and $N$ are Hilbert $A$-modules, $M$…

Let ${\cal A}_1$ be the class of all unital separable simple $C^*$-algebras $A$ such that $A\otimes U$ has tracial rank at most one for all UHF-algebras of infinite type. It has been shown that amenable ${\cal Z}$-stable $C^*$-algebras in…

Consider a product system over the positive cone of a quasi-lattice ordered group. We construct a Fell bundle over an associated groupoid so that the cross-sectional algebra of the bundle is isomorphic to the Nica-Toeplitz algebra of the…

It is shown that a C*-algebra generated by any faithful covariant representation of a Hilbert bimodule X is canonically isomorphic to the crossed product associated to X provided that Rieffel's induced representation functor X-ind is…

For $ C^*$-algebras $ \mathfrak{A}, A$ and $ B $ where $ A $ and $ B $ are $ \mathfrak{A} $-bimodules with compatible actions, we consider amalgamated $ \mathfrak{A} $-module tensor product of $ A $ and $ B $ and study its relation with the…

We find first structural background information about the reasons that for any C*-algebra $A$ and any two Hilbert $A$-modules $M \subseteq N$ with $M^\perp=\{0\}$, every bounded $A$-linear map $N \to A$ (or $N \to N)$ vanishing on $M$ might…

This paper deals with a "naive" way of generalization of the Kazhdan's property (T) to C*-algebras. This approach differs from the approach of Connes and Jones, which has already demonstrated its utility. Nevertheless it turned out that our…

Let U, V, and W be multiplicative unitaries coming from discrete Kac systems such that W is an amenable normal submultiplicative unitary of V with quotient U. We define notions for right-Hilbert bimodules of coactions of S_V and (S_V)^,…

We prove the index theorem for elliptic operators acting on sections of bundles where fiber is equal to a projective module over a C*-algebra, in the situation of action of a compact Lie group on this algebra as well as on the total space…

We construct a new class of finite-dimensional C^*-quantum groupoids at roots of unity q=e^{i\pi/\ell}, with limit the discrete dual of the classical SU(N) for large orders. The representation category of our groupoid turns out to be tensor…

We prove that every coaction of a compact group on a finite-dimensional $C^*$-algebra is associated with a Fell bundle. Every coaction of a compact group on a matrix algebra is implemented by a unitary operator. A coaction of a compact…

Let $A$ and $B$ be $\sigma$-unital $C^*$-algebras and $X$ and $Y$ an $A-A$-equivalence bimodule and a $B-B$-equivalence bimodule, respectively. Also, let $A\rtimes_X \mathbb{Z}$ and $B\rtimes_Y \mathbb{Z}$ be the crossed products of $A$ and…

We present an explicit formula for the $K$-theory of the $C^*$-algebra associated with a relative generalized Boolean dynamical system $(\CB, \CL, \theta, \CI_\af; \CJ)$. In particular, we find concrete generators for the $K_1$-group of…

Using the machinery of weak fibration categories due to Schlank and the first author, we construct a convenient model structure on the pro-category of separable $C^*$-algebras $\mathrm{Pro}(\mathtt{SC^*})$. The opposite of this model…

In this paper, we will prove that if $A$ is a $C^*$-algebra with an effective coaction $\epsilon$ by a compact quantum group, then the fixed point algebra and the reduced crossed product are Morita equivalent. As an application, we prove an…