Related papers: Exotic group C*-algebras in noncommutative duality

If a locally compact group G acts on a C*-algebra B, we have both full and reduced crossed products, and each has a coaction of G. We investigate "exotic" coactions in between, that are determined by certain ideals E of the…

We consider group actions of topological groups on C*-algebras of the types which occur in many physics models. These are singular actions in the sense that they need not be strongly continuous, or the group need not be locally compact. We…

We investigate the representation theory of the crossed-product C*-algebra associated to a compact group G acting on a locally compact space X when the stability subgroups vary discontinuously. Our main result applies when G has a principal…

We show that the category A(G) of actions of a locally compact group G on C*-algebras (with equivariant nondegenerate *-homomorphisms into multiplier algebras) is equivalent, via a full-crossed-product functor, to a comma category of…

Let a discrete group $G$ act on a unital simple C$^*$-algebra $A$ by outer automorphisms. We establish a Galois correspondence $H\mapsto A\rtimes_{\alpha,r}H$ between subgroups of $G$ and C$^*$-algebras $B$ satisfying $A\subseteq B…

We consider the following problem. Suppose $\alpha$ is an action of a locally compact group $G$ on a $C^*$-algebra $A$, $H$ is a closed subgroup of $G$, and $(\pi,U)$ is a covariant representation of $(A,H,\alpha)$. For which closed…

An exotic crossed product is a way of associating a C*-algebra to each C*-dynamical system that generalizes the well-known universal and reduced crossed products. Exotic crossed products provide natural generalizations of, and tools to…

We study the C*-algebra crossed product $C_0(X)\rtimes G$ of a locally compact group $G$ acting properly on a locally compact Hausdorff space $X$. Under some mild extra conditions, which are automatic if $G$ is discrete or a Lie group, we…

We obtain a Galois correspondence between the lattice of intermediate C*-discrete subalgebras intermediate to a given irreducible C*-discrete inclusion, and characterize these as targets of compatible expectations under a traciality…

Let $P$ be a unital subsemigroup of a group $G$. We propose an approach to $\mathrm{C}^*$-algebras associated to product systems over $P$. We call the $\mathrm{C}^*$-algebra of a given product system $\mathcal{E}$ its covariance algebra and…

We decompose the crossed product functor for actions of crossed modules of locally compact groups on C*-algebras into more elementary constructions: taking crossed products by group actions and fibres in C*-algebras over topological spaces.…

I combine recent results in the structure theory of nuclear C*-algebras and in topological dynamics to classify certain types of crossed products in terms of their Elliott invariants. In particular, transformation group C*-algebras…

Exotic group $C^*$-algebras are $C^*$-algebras that lie between the universal and the reduced group $C^*$-algebra of a locally compact group. We consider simple Lie groups $G$ with real rank one and investigate their exotic group…

Given a weak Kac system with duality $(\mathcal{H},V,U)$ arising from regular $\mathrm{C}^{*}$-algebraic locally compact quantum group $(\mathcal{G},\Delta)$, a $\mathrm{C}^{*}$-algebra $A$, and a sufficiently well-behaved coaction…

We show that for a C*-algebra A and a discrete group G with an action of G on A, the reduced crossed product C*-algebra possesses a natural generalization of the convolution product, which we suggest should be named the Hadamard product. We…

In this paper, we define the notions of full pro-$C^{*}$-crossed product, respectively reduced pro-$C^{*}$-crossed product, of a pro-$C^{*}$-algebra $A[\tau_{\Gamma}] $ by a strong bounded action $\alpha$ of a locally compact group $G$ and…

We survey the results required to pass between full and reduced coactions of locally compact groups on C*-algebras, which say, roughly speaking, that one can always do so without changing the crossed-product C*-algebra. Wherever possible we…

We construct the crossed product of a C(X)-algebra by an endomorphism, in such a way that the endomorphism itself becomes induced by the bimodule of continuous sections of a vector bundle. Some motivating examples for such a construction…

We investigate the C*-algebra inclusions $B \subset A \rtimes_{\rm r} \Gamma$ arising from inclusions $B \subset A$ of $\Gamma$-C*-algebras. The main result shows that, when $B \subset A$ is C*-irreducible in the sense of R{\o}rdam, and is…

Let $\alpha : \Gamma \curvearrowright A$ be an action of a discrete group $\Gamma$ on a unital C*-algebra $A$ by *-automorphisms and let $A \rtimes_{\alpha,\lambda} \Gamma$ denote the corresponding reduced crossed product C*-algebra.…