Related papers: Quasidiagonal traces on exact $C^\ast$-algebras

We generalise recent results about quasi-Cartan, Cartan and diagonal subalgebras by introducing graded versions. We show that there is a correspondence between graded algebraic quasi-Cartan/ Cartan/ diagonal pairs and certain graded twisted…

We observe almost divisibility for the original Cuntz semigroup of a simple AH algebra with strict comparison. As a consequence, the properties of strict comparison, finite nuclear dimension, and Z-stability are equivalent for such…

We compute Picard groups of several nuclear and non-nuclear simple stably projectionless C*-algebras. In particular, the Picard group of Razak-Jacelon algebra W_2 is isomorphic to a semidirect product of Out(W_2) with R_+^\times. Moreover,…

We associate cube complexes called completions to each subgroup of a right-angled Coxeter group (RACG). A completion characterizes many properties of the subgroup such as whether it is quasiconvex, normal, finite-index or torsion-free. We…

We give a detailed introduction to the theory of Cuntz semigroups for C*-algebras. Beginning with the most basic definitions and technical lemmas, we present several results of historical importance, such as Cuntz's theorem on the existence…

We prove that Z-stable, simple, separable, nuclear, non-unital C*-algebras have nuclear dimension at most 1. This completes the equivalence between finite nuclear dimension and Z-stability for simple, separable, nuclear, non-elementary…

Let $\mathcal A$ be a separable, unital, approximately divisible C$^*$-algebra. We show that $\mathcal A$ is generated by two self-adjoint elements and the topological free entropy dimension of any finite generating set of $\mathcal A$ is…

Elliott and Kucerovsky stated that a non-unital extension of separable $C^\ast$-algebras with a stable ideal, is nuclearly absorbing if and only if the extension is purely large. However, their proof was flawed. We give a counter example to…

In this paper, we present an explicit construction of twisted traces for quantum Coulomb branches of conical theories. We develop an operator representation of the Coulomb branch algebra and use it to derive integral formulas for the…

It is shown that the coloured isomorphism class of a unital, simple, $\mathcal{Z}$-stable, separable amenable C$^*$-algebra satisfying the Universal Coefficient Theorem (UCT) is determined by its tracial simplex.

Let $A$ be an amenable separable \CA and $B$ be a non-unital but $\sigma$-unital simple \CA with continuous scale. We show that two essential extensions $\tau_1$ and $\tau_2$ of $A$ by $B$ are approximately unitarily equivalent if and only…

We establish the tracial stability of a certain class of graph products of C*-algebras. This result involves the development of the "pincushion class" of finite graphs. We then apply this result in two ways. The first application yields a…

We exhibit a countably infinite family of simple, separable, nuclear, and mutually non-isomorphic C*-algebras which agree on K-theory and traces. The algebras do not absorb the Jiang-Su algebra Z tensorially, answering a question of N. C.…

In this note we address a question of Don Hadwin: "Which groups have strongly quasidiagonal C*-algebras?" In recent work we showed that all finitely generated virtually nilpotent groups have strongly quasidiagonal C*-algebras, while…

The categories of almost modules and almost algebras are introduced as a convenient setting for the development of Faltings' method of almost etale extensions. After some preliminaries of general "almost homological algebra" we construct…

In this paper, we introduce some classes of generalized tracial approximation ${\rm C^*}$-algebras. Consider the class of unital ${\rm C^*}$-algebras which are tracially $\mathcal{Z}$-absorbing (or have tracial nuclear dimension at most…

Nuclear C*-algebras enjoy a number of approximation properties, most famously the completely positive approximation property. This was recently sharpened to arrange for the incoming maps to be sums of order-zero maps. We show that, in…

We extend in this paper the characterisation of a separable nuclear \cst-algebra given by Kirchberg proving that given a unital separable continuous field of nuclear C*-algebras A over a compact metrizable space X, the C(X)-algebra A is…

For every Hecke C*-algebra of right-angled, hyperbolic type, we construct a smooth subalgebra to which traces associated with arbitrary conjugacy classes in the associated Coxeter group extend. We calculate the pairing with K-theory of the…

We investigate the notion of tracial $\mathcal Z$-stability beyond unital C*-algebras, and we prove that this notion is equivalent to $\mathcal Z$-stability in the class of separable simple nuclear C*-algebras.