Related papers: Traceless AF embeddings and unsuspended $E$-theory

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…

A finite-dimensional Lie algebra $L$ over a field $F$ of characteristic zero is called elementary if each of its subalgebras has trivial Frattini ideal; it is an $A$-algebra if every nilpotent subalgebra is abelian. This paper is a…

The notion of isomorphism of stable AF-C*-algebras is considered in this paper in the case when the corresponding Bratteli diagram is stationary, i.e., is associated with a single square primitive nonsingular incidence matrix.…

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…

We characterize the class of RFD $C^*$-algebras as those containing a dense subset of elements that attain their norm under a finite-dimensional representation. We show further that this subset is the whole space precisely when every…

Any algebra herein is intended over a field of characteristic 0. Let $E$ denote the infinite dimensional Grassman algebra. Given a power associative finite dimensional {$\mathbb{Z}_2$-graded-central-simple} $A$ and a supertrace algebra $B$,…

A trace $\tau$ on a separable C*-algebra $A$ is called matricial field (MF) if there is a trace-preserving morphism from $A$ to $Q_\omega$, where $Q_\omega$ denotes the norm ultrapower of the universal UHF-algebra $Q$. In general, the trace…

We examine the question of quasidiagonality for C*-algebras of discrete amenable groups from a variety of angles. We give a quantitative version of Rosenberg's theorem via paradoxical decompositions and a characterization of…

For a discrete group $G$, we consider certain ideals $\mathcal{I}\subset c_0(G)$ of sequences with prescribed rate of convergence to zero. We show that the equality between the full group C$^\ast$-algebra of $G$ and the C$^\ast$-completion…

We present a conjecture on the irreducibility of the tensor products of fundamental representations of quantized affine algebras. This conjecture implies in particular that the irreducibility of the tensor products of fundamental…

It is shown that the pairing of the K00 group of a C*-algebra with the densely defined traces of the algebra can be extended to a pairing with the densely defined weights. For traces the pairing can be extended to the K0 group without the…

For a number of properties of C*-algebras, including real rank zero, stable rank one, pure infiniteness, residual hereditary infiniteness, the combination of pure infiniteness and the ideal property, the property of being an AT algebra with…

We prove that separable C*-algebras which are completely close in a natural uniform sense have isomorphic Cuntz semigroups, continuing a line of research developed by Kadison - Kastler, Christensen, and Khoshkam. This result has several…

We introduce the notion of locally finite decomposition rank, a structural property shared by many stably finite nuclear C*-algebras. The concept is particularly relevant for Elliott's program to classify nuclear C*-algebras by K-theory…

We prove that all finite W-algebras associated with nilpotent elements e in a complex semisimple Lie algebra g have finite-dimensional representations. In order to obtain this result we establish a connection between primitive ideals of…

The completely positive rank is an analogue of topological covering dimension, defined for nuclear C*-algebras via completely positive approximations. These may be thought of as simplicial approximations of the algebra, which leads to the…

In this note, we will show that the twisted convolution algebra $L^1_{\alpha,\omega}({\sf G},\mathfrak A)$ associated to a twisted action of a locally compact group ${\sf G}$ on a $C^*$-algebra $\mathfrak A$ has the following property:…

We study the validity of the Blackadar-Kirchberg conjecture for extensions of separable, nuclear, quasidiagonal $C^*$-algebras that satisfy the UCT. More specifically, we show that the conjecture for the extension has an affirmative answer…

In this paper, we prove that if $\mathcal{A}$ is a unital separable $C^*$-algebra, $\mathcal{M}$ is a von Neumann algebra which has the Kirchberg's quotient weak expectation property (QWEP), and $\phi:\, \mathcal{A}\rightarrow \mathcal{M}$…

We present a classification theorem for amenable simple stably projectionless C*-algebras with generalized tracial rank one whose $K_0$ vanish on traces which satisfy the Universal Coefficient Theorem. One of them is denoted by ${\cal Z}_0$…