Related papers: Robinson forcing and the quasidiagonality problem
We prove that faithful traces on separable and nuclear C*-algebras in the UCT class are quasidiagonal. This has a number of consequences. Firstly, by results of many hands, the classification of unital, separable, simple and nuclear…
This is a survey of recent progress in the structure and classification theory of nuclear C*-algebras. In particular, I outline how the Universal Coefficient Theorem ensures a positive answer to the quasidiagonality question in the presence…
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 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…
C*-algebras are rings, sometimes nonunital, obeying certain axioms that ensure a very well-behaved representation theory upon Hilbert space. Moreover, there are some well-known features of the representation theory leading to subtle…
We solve a class of lifting problems involving approximate polynomial relations (soft polynomial relations). Various associated C*-algebras are therefore projective. The technical lemma we need is a new manifestation of Akemann and…
In recent years, a large class of nuclear $C^\ast$-algebras have been classified, modulo an assumption on the Universal Coefficient Theorem (UCT). We think this assumption is redundant and propose a strategy for proving it. Indeed,…
A trace on a C*-algebra is amenable (resp. quasidiagonal) if it admits a net of completely positive, contractive maps into matrix algebras which approximately preserve the trace and are approximately multiplicative in the 2-norm (resp.…
We give a detailed survey of the theory of quasidiagonal C*-algebras. The main structural results are presented and various functorial questions around quasidiagonality are discussed. In particular we look at what is currently known (and…
Let $R$ be a domain and $B=R[x_1^{\pm1},\ldots,x_n^{\pm1}]$ the Laurent polynomial ring over $R$. In this paper we study pre-factorially closed (pfc) and quasi-factorially closed (qfc) $R$-subalgebras of $B$, which generalize the notion of…
We show that outer approximately represenbtable actions of a finite cyclic group on UCT Kirchberg algebras satisfy a certain quasi-freeness type property if the corresponding crossed products satisfy the UCT and absorb a suitable UHF…
I give an overview of recent developments in the structure and classification theory of separable, simple, nuclear C*-algebras. I will in particular focus on the role of quasidiagonality and amenability for classification, and on the…
We prove that every unital stably finite simple amenable $C^*$-algebra $A$ with finite nuclear dimension and with UCT such that every trace is quasi-diagonal has the property that $A\otimes Q$ has generalized tracial rank at most one, where…
The mid-seventies' works on C*-algebras of Brown-Douglas-Fillmore and Elliott both contained uniqueness and existence results in a now standard sense. These papers served as keystones for two separate theories -- KK-theory and the…
In this paper, we consider Blackadar and Kirchberg's MF algebras. We show that any inner quasidiagonal C-algebra is MF algebra and we generalize Voiculescu's Representation Theorem for a special version of MF algebras. Moreover, we define a…
Our work proposes a unified approach to three different topics in a general Riemannian setting: splitting theorems, symmetry results and overdetermined elliptic problems. By the existence of a stable solution to the semilinear equation…
In the paper, we consider the question whether a unital full amalgamated free product of quasidiagonal C*-algebras is quasidiagonal again. We give a sufficient condition such that a unital full amalgamated free product of quasidiagonal…
We consider a version of a famous open problem formulated by Kadison, asking whether bounded representations of operator algebras are automatically completely bounded. We investigate this question in the context of amenable operator…
In this work it is shown that certain interesting types of quasi-orthogonal system of subalgebras (whose existence cannot be ruled out by the trivial necessary conditions) cannot exist. In particular, it is proved that there is no…
We conjecture that a unital C$^*$-algebra is a W$^*$-algebra if and only if each of its maximal abelian self-adjoint subalgebras is a W$^*$-algebra; this is a space-free analogue of a known result due to G.K. Pedersen. Our main result is a…