Related papers: On the inclusion $\cO_2 \subset \cQ_2$

C*-algebras generalizing Cuntz-Krieger algebras can be associated to hyperbolic homeomorphisms of compact metric spaces. They satisfy a non-commutative form of Spanier-Whitehead duality with respect to K-theory. We prove this for the case…

We consider two Z/2Z-actions on the Podles generic quantum spheres. They yield, as noncommutative quotient spaces, the Klimek-Lesniewski q-disc and the quantum real projective space, respectively. The C*-algebras of all these quantum spaces…

We prove the existence of a C*-diagonal in the Cuntz algebra O_2 with spectrum homeomorphic to the Cantor space.

We discuss the existence of (injectively) universal C*-algebras and prove that all C*-algebras of density character $\aleph_1$ embed into the Calkin algebra, $Q(H)$. Together with other results, this shows that each of the following…

We describe a class of $C^*$-algebras which simultaneously generalise the ultragraph algebras of Tomforde and the shift space $C^*$-algebras of Matsumoto. In doing so we shed some new light on the different $C^*$-algebras that may be…

We construct the first example of a $C^*$-algebra $A$ with the properties in the title. This gives a new example of non-nuclear $A$ for which there is a unique $C^*$-norm on $A \otimes A^{op}$. This example is of particular interest in…

We give a sufficient condition for a $^*$-algebra with a specified basis to have an enveloping $C^*$-algebra. Particularizing to the setting of a Hecke algebra $\h(G,\gm)$, we show that under a suitable assumption not only we can assure…

For a closed subgroup of a locally compact group the Rieffel induction process gives rise to a $C^*$-correspondence over the $C^*$-algebra of the subgroup. We study the associated Cuntz-Pimsner algebra and show that, by varying the subgroup…

We define an admissible decomposition of a graph $E$ into subgraphs $F_1$ and $F_2$, and consider the intersection graph $F_1\cap F_2$ as a subgraph of both $F_1$ and $F_2$. We prove that, if the graph $E$ is row finite and its…

We examine rigidity phenomena for representations of amenable operator algebras which have an ideal of compact operators. We establish that a generalized version of Kadison's conjecture on completely bounded homomorphisms holds for the…

In this memoir we develop a framework to study rigidity problems for Roe-like C*-algebras of countably generated coarse spaces. The main goal is to give a complete and self-contained solution to the problem of C*-rigidity for proper…

In this paper we study Cuntz--Pimsner algebras associated to $\mathrm{C}^*$-correspondences over commutative $\mathrm{C}^*$-algebras from the point of view of the $\mathrm{C}^*$-algebra classification programme. We show that when the…

Motivated by Exel's inverse semigroup approach to combinatorial C*-algebras, in a previous work the authors defined an inverse semigroup associated with a labelled space. We construct a representation of the C*-algebra of a labelled space,…

We introduce and analyse the structure of C*-algebras arising from ideals in right tensor C*-precategories, which naturally generalize both relative Cuntz-Pimsner and Doplicher-Roberts algebras. We establish an explicit intrinsic…

In this paper we generalize the notion of a $k$-graph into (countable) infinite rank. We then define our $C^*$-algebra in a similar way as in $k$-graph $C^*$-algebras. With this construction we are able to find analogues to the Gauge…

In this paper we describe all surjective isometries between open subgroups of the groups of invertible elements in unital $C^{*}$-algebras.

In this paper we continue the analysis undertaken in a series of previous papers on structures arising as completions of C*-algebras under topologies coarser that their norm and we focus our attention on the so-called {\em locally convex…

The note is concerned with inductive systems of Toeplitz algebras and their $*$-homomorphisms over arbitrary partially ordered sets. The Toeplitz algebra is the reduced semigroup $C^*$-algebra for the additive semigroup of non-negative…

It is shown that every linear strong Birkhoff-James isomorphism between unital $C^*$-algebras is a $*$-isomorphism followed by a unitary multiplication. Moreover, as a partial extension of this result to the non-unital case, the form of…

Every $\mathrm{C}^*$-algebra, regardless of its density character, can be embedded into the Calkin algebra in a forcing extension of the universe obtained without collapsing any cardinal.