Related papers: Continuous Fields of Kirchberg C*-algebras

We classify unital monomorphisms into certain simple Z-stable C^*-algebras up to approximate unitary equivalence. The domain algebra C is allowed to be any unital separable commutative C^*-algebra, or any unital simple separable nuclear…

We generalize the notion of a continuous field of C*-algebras to that of Hilbert C*-bimodules. Given a partially ordered set $P$ and a monotonically non-decreasing family of ternary rings of operators (TROs) assigned to the points of $P$,…

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 geometrically describe the relation induced on a set of graphs by isomorphism of their associated graph C*-algebras as the smallest equivalence relation generated by five types of moves. The graphs studied have finitely many vertices and…

We present the first range result for the total K-theory of C*-algebras. This invariant has been used successfully to classify certain separable, nuclear C*-algebras of real rank zero. Our results complete the classification of the…

A $C^*$-algebra satisfies the Universal Coefficient Theorem (UCT) of Rosenberg and Schochet if it is equivalent in Kasparov's $KK$-theory to a commutative $C^*$-algebra. This paper is motivated by the problem of establishing the range of…

Extending the work of Cuntz and Vershik, we develop a general notion of independence for commuting group endomorphisms. Based on this concept, we initiate the study of irreversible algebraic dynamical systems, which can be thought of as…

We augment Restorff's classification of purely infinite Cuntz-Krieger algebras by describing the range of his invariant on purely infinite Cuntz-Krieger algebras. We also describe its range on purely infinite graph C*-algebras with finitely…

We use $K$-theory of the $C^*$-algebras to study the Arakelov geometry, i.e. a compactification of the arithmetic schemes $V\to Spec ~\mathbf{Z}$. In particular, it is proved that the Picard group of $V$ is isomorphic to the $K_0$-group of…

We show that C*-algebras generated by irreducible representations of finitely generated nilpotent groups satisfy the universal coefficient theorem of Rosenberg and Schochet. This result combines with previous work to show that these…

The notion of bounded element of C*-inductive locally convex spaces (or C*-inductive partial *-algebras) is introduced and discussed in two ways: the first one takes into account the inductive structure provided by certain families of…

We define the filtrated K-theory of a C*-algebra over a finite topological space X and explain how to construct a spectral sequence that computes the bivariant Kasparov theory over X in terms of filtrated K-theory. For finite spaces with…

Complexity rank for $C^*$-algebras was introduced by the second author and Yu for applications towards the UCT: very roughly, this rank is at most $n$ if you can repeatedly cut the $C^*$-algebra in half at most $n$ times, and end up with…

We study the K-theory of ring C*-algebras associated to rings of integers in global function fields with only one single infinite place. First, we compute the torsion-free part of the K-groups of these ring C*-algebras. Secondly, we show…

We consider finite approximations of a topological space $M$ by noncommutative lattices of points. These lattices are structure spaces of noncommutative $C^*$-algebras which in turn approximate the algebra $\cc(M)$ of continuous functions…

We determine the injective envelope and local multiplier algebra of a continuous trace C*-algebra that arises from a continuous Hilbert bundle over an arbitrary locally compact Hausdorff space. In addition, we show that the second-order…

We continue the study of the effective content of $K$-theory for C*-algebras, with a focus on AF algebras. We show that from a c.e. presentation of an AF algebra it is possible to compute a representation of the algebra as an inductive…

The structure of the $C^*$-algebras corresponding to even-dimensional mirror quantum spheres is investigated. It is shown that they are isomorphic to both Cuntz-Pimsner algebras of certain $C^*$-correspondences and $C^*$-algebras of certain…

Let $X$ be a locally compact non compact Hausdorff topological space. Consider the algebras $C(X)$, $C_b(X)$, $C_0(X)$, and $C_{00}(X)$ of respectively arbitrary, bounded, vanishing at infinity, and compactly supported continuous functions…

We observe that a recent theorem of Sato, Toms-White-Winter and Kirchberg-Rordam also holds for certain nonunital C*-algebras. Namely, we show that an algebraically simple, separable, nuclear, nonelementary C*-algebra with strict…