Related papers: C_0(X)-algebras, stability and strongly self-absor…

We show that a simple separable unital nuclear nonelementary $C^*$-algebra whose tracial state space has a compact extreme boundary with finite covering dimension admits uniformly tracially large order zero maps from matrix algebras into…

Let $A$ be an algebraically simple, separable, nuclear, $\mathcal{Z}$-stable $C^*$-algebra for which the trace space $T(A)$ is a Bauer simplex and the extremal boundary $\partial_e T(A)$ has finite covering dimension. We prove that each…

Let A be an approximately subhomogeneous (ASH) C*-algebra with slow dimension growth. We prove that if A is unital and simple, then the Cuntz semigroup of A agrees with that of its tensor product with the Jiang-Su algebra Z. In tandem with…

The cone of lower semicontinuous traces is studied with a view to its use as an invariant. Its properties include compactness, Hausdorffness, and continuity with respect to inductive limits. A suitable notion of dual cone is given. The cone…

We define centrally large subalgebras of simple unital C*-algebras, strengthening the definition of large subalgebras in previous work. We prove that if A is any infinite dimensional simple separable unital C*-algebra which contains a…

We prove that a factorial tracially complete C*-algebra with CPoU has real rank zero and stable rank one. This leads to an essentially complete description of the Cuntz semigroup of these algebras. In particular, the results of this paper…

Let $X$ be an infinite compact metrizable space, and let $\sigma: X\to X$ be a minimal homeomorphism. Suppose that $(X, \sigma)$ has zero mean topological dimension. The associated C*-algebra $A=\mathrm{C}(X)\rtimes_\sigma\mathbb Z$ is…

We provide a shorter new proof of the fact that Z-stable C*-algebras are K1-surjective using the R{\o}rdam-Winter picture of the Jiang-Su algebra Z. Consequently, we recapture the K-stability of Z-stable C*-algebras.

We study the class of pseudocompact C*-algebras, which are the logical limits of finite-dimensional C*-algebras. The pseudocompact C*-algebras are unital, stably finite, real rank zero, stable rank one, and tracial. We show that the…

Let Z denote the simple limit of prime dimension drop algebras that has a unique tracial state. Let A != 0 be a unital C^*-algebra with A = A tensor Z. Then the homotopy groups of the group U(A) of unitaries in A are stable invariants,…

We characterize stability of graph C*-algebras by giving five conditions equivalent to their stability. We also show that if G is a graph with no sources, then C*(G) is stable if and only if each vertex in G can be reached by an infinite…

Simple, separable, unital, monotracial and nuclear C$^*$-algebras are shown to have finite nuclear dimension whenever they absorb the Jiang-Su algebra $\mathcal{Z}$ tensorially. This completes the proof of the Toms-Winter conjecture in the…

For a locally compact group $G$ and a strongly self-absorbing $G$-algebra $(\mathcal{D},\delta)$, we obtain a new characterization of absorption of a strongly self-absorbing action using almost equivariant completely positive maps into the…

We show that the Fra\"iss\'e limit of a category of unital separable $C^*$-algebras which is sufficiently closed under tensor products of its objects and morphisms is strongly self-absorbing, given that it has approximate inner half-flip.…

Any unital separable continuous C(X)-algebra with properly infinite fibres is properly infinite as soon as the compact Hausdorff space X has finite topolog-ical dimension. We study conditions under which this is still the case if the…

We prove that a graph C*-algebra with exactly one proper nontrivial ideal is classified up to stable isomorphism by its associated six-term exact sequence in K-theory. We prove that a similar classification also holds for a graph C*-algebra…

We study properties of the central sequence algebra of a C*-algebra, and we present an alternative approach to a recent result of Matui and Sato. They prove that every unital separable simple nuclear C*-algebra, whose trace simplex is…

We consider a certain class of unital simple stably finite C^*-algebras which absorb the Jiang-Su algebra Z tensorially. Under a mild assumption, we show that the crossed product of a C^*-algebra in this class by a strongly outer action of…

It is shown that projectionless C*-algebras that tensorially absorb the Jiang-Su algebra have the property that every element is a limit of products of two nilpotents. This is then used to classify the approximate unitary equivalence…

We construct a simple, nuclear, stably projectionless C*-algebra W which has trivial K-theory and a unique tracial state, and we investigate the extent to which W might fit into the hierarchy of strongly self-absorbing C*-algebras as an…