Related papers: On $\mathrm{C}^*$-algebras associated to product s…

We study uniform perturbations of crossed product C$^*$-algebras by amenable groups. Given a unital inclusion of C$^*$-algebras $C\subseteq D$ and sufficiently close separable intermediate C$^*$-subalgebras $A$, $B$ for this inclusion with…

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…

If $G$ acts on a $C^*$-correspondence ${\mathcal H}$, then by the universal property $G$ acts on the Cuntz-Pimsner algebra ${\mathcal O}_{\mathcal H}$ and we study the crossed product ${\mathcal O}_{\mathcal H}\rtimes G$ and the fixed point…

To each discrete product system E of finite-dimensional Hilbert spaces we associate a C*-algebra O_E. When E is the n-dimensional product system over N, O_E is the Cuntz algebra O_n, and the irrational rotation algebras appear as O_E for…

C*-quantum groups with projection are the noncommutative analogues of semidirect products of groups. Radford's Theorem about Hopf algebras with projection suggests that any C*quantum group with projection decomposes uniquely into an…

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…

Motivated by reformulating Furstenberg's $\times p,\times q$ conjecture via representations of a crossed product $C^*$-algebra, we show that in a discrete $C^*$-dynamical system $(A,\Gamma)$, the space of (ergodic) $\Gamma$-invariant states…

Topological quivers generalize the notion of directed graphs in which the sets of vertices and edges are locally compact (second countable) Hausdorff spaces. Associated to a topological quiver $Q$ is a $C^*$-correspondence, and in turn, a…

We present a systematic study of the structure of crossed products and fixed point algebras by compact group actions with the Rokhlin property on not necessarily unital C*-algebras. Our main technical result is the existence of an…

This is a sequel to our paper on nonlinear completely positive maps and dilation theory for real involutive algebras, where we have reduced all representation classification problems to the passage from a $C^*$-algebra ${\mathcal A}$ to its…

In this paper we construct and study the representation theory of a Hopf C^*-algebra with approximate unit, which constitutes quantum analogue of a compact group C^*-algebra. The construction is done by first introducing a…

Given a group G, we construct, in a canonical way, an inverse semigroup S(G) associated to G. The actions of S(G) are shown to be in one-to-one correspondence with the partial actions of G, both in the case of actions on a set, and that of…

We give a definition of partition C*-algebras: To any partition of a finite set, we assign algebraic relations for a matrix of generators of a universal C*-algebra. We then prove how certain relations may be deduced from others and we…

We solve a class of lifting problems involving approximate polynomial relations (soft polynomial relations). Various associated C*-algebras are therefore projective. The technical lemma we need is a new manifestation of Akemann and…

We study isometric representations of product systems of correspondences over the semigroup $\mathbb{N}^k$ which are minimal dilations of finite dimensional, fully coisometric representations. We show the existence of a unique minimal…

We start by reviewing the relation between toposes and Grothendieck quantales. We improve results of previous work on this relation by giving both a characterisation of the map from the tensor product of two internal sup-lattices to another…

We introduce crossed products of a $C^*$-algebra $A$ by a completely positive map $\varrho:A\to A$ relative to an ideal in $A$. They generalize various crossed products by endomorphisms when $\varrho$ is multiplicative. When $A$ is…

We describe simplicity of the Stacey crossed product A\times_\beta \N in terms of conditions of the endomorphism \beta. Then, we use a characterization of the graph C*-algebras C*(E) as the Stacey crossed product…

We compute the K-theory for C*-algebras naturally associated with rings of integers in number fields. The main ingredient is a duality theorem for arbitrary global fields. It allows us to identify the crossed product arising from affine…

Exploiting the graph product structure and results concerning amalgamated free products of C*-algebras we provide an explicit computation of the K-theoretic invariants of right-angled Hecke C*-algebras, including concrete algebraic…