Related papers: Classification of $\mathcal O_\infty$-stable $C^\a…

We prove that if a connected and simply connected Lie group $G$ admits connected closed normal subgroups $G_1\subseteq G_2\subseteq \cdots \subseteq G_m=G$ with $\dim G_j=j$ for $j=1,\dots,m$, then its group $C^*$-algebra has closed…

We give a complete classification of the ideals of the core of the C*-algebras associated with self-similar maps under a certain condition. Any ideal is completely determined by the intersection with the coefficient algebra C(K) of the…

We show that certain extensions of classifiable C*-algebra are strongly classified by the associated six-term exact sequence in K-theory together with the positive cone of K_{0}-groups of the ideal and quotient. We apply our result to give…

In this article I study a number of topological and algebraic dimension type properties of simple C*-algebras and their interplay. In particular, a simple C*-algebra is defined to be (tracially) (m,\bar{m})-pure, if it has (strong tracial)…

We show that every groupoid C*-algebra is isomorphic to its opposite, and deduce that there exist C*-algebras that are not stably isomorphic to groupoid C*-algebras, though many of them are stably isomorphic to twisted groupoid C*-algebras.…

We study the local operator space structure of nuclear $C^*$-algebras. It is shown that a $C^*$-algebra is nuclear if and only if it is an $\OL_{\infty, \la}$ space for some (and actually for every) $\la > 6$. The $\OL_\infty$ constant…

We describe a proof of the following folklore theorem: If $\cX = G/K$ is the homogeneous space of a simply connected compact semisimple Lie group with Poisson-Lie stabilizers, then the $q$-deformed algebras of regular functions $\CC[\cX_q]$…

Let A and B be separable nuclear continuous C(X)-algebras over a finite dimensional compact metrizable space X. It is shown that an element $\sigma$ of the parametrized Kasparov group KK_X(A,B) is invertible if and only if all its fiberwise…

For every algebraically closed field $\boldsymbol k$ of characteristic different from $2$, we prove the following: (1) Generic finite dimensional (not necessarily associative) $\boldsymbol k$-algebras of a fixed dimension, considered up to…

We complete the classification of Bost--Connes systems. We show that two Bost--Connes C*-algebras for number fields are isomorphic if and only if the original semigroups actions are conjugate. Together with recent reconstruction results in…

Suppose that $\mathcal M$ is a countably decomposable type II$_1$ von Neumann algebra and $\mathcal A$ is a separable, non-nuclear, unital C$^*$-algebra. We show that, if $\mathcal M$ has Property $\Gamma$, then the similarity degree of…

A profinite group is index-stable if any two isomorphic open subgroups have the same index. Let $p$ be a prime, and let $G$ be a compact $p$-adic analytic group with associated $\mathbb{Q}_p$-Lie algebra $\mathcal{L}(G)$. We prove that $G$…

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…

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…

It is shown that the dual $\hat{A}$ of a separable $C^{\ast}$-algebra $A$ is discrete if and only if its Banach space dual has the weak$^{\ast}$-fixed point property. We prove further that these properties are equivalent to the uniform…

Let $G$ be a compact connected Lie group and $K$ a closed connected subgroup. Assume that the order of any torsion element in the integral cohomology of $G$ and $K$ is invertible in a given principal ideal domain $k$. It is known that in…

Let A and B be $C^*$-algebras, A separable, and B $\sigma$-unital and stable. It is shown that there are natural isomorphisms $E(A,B)=KK(SA,Q(B))=[SA,Q(B)\otimes K]$, where $SA=C_0(0,1)\otimes A$, $[\cdot,\cdot]$ denotes the set of homotopy…

Given an arbitrary countable ordinal $\alpha $, we introduce the notion of type $I_{\alpha }$ C*-algebra and $\alpha $-subhomogeneous C*-algebra. When $\alpha =0$, these recover the notions of Fell C*-algebra and of commutative C*-algebra,…

We provide a complete classification of the class of unital graph $C^*$-algebras - prominently containing the full family of Cuntz-Krieger algebras - showing that Morita equivalence in this case is determined by ordered, filtered…

We prove that the twisted group C*-algebra of a finitely generated nilpotent group is $\mathcal{Z}$-stable if and only if it is nowhere scattered, a condition that we characterize in terms of the given group and 2-cocycle. As a main…