Related papers: On the classification problem for nuclear C*-algeb…

We construct a simple C*-algebra with nuclear dimension zero that is not isomorphic to its tensor product with the Jiang-Su algebra Z, and a hyperfinite II_1 factor not isomorphic to its tensor product with the separable hyperfinite II_1…

We construct an example of a simple approximately homogeneous C*-algebra such that its Elliott invariant admits an automorphism which is not induced by an automorphism of the algebra.

We show that if $A$ is $\mathcal{Z}$, $\mathcal{O}_2$, $\mathcal{O}_{\infty}$, a UHF algebra of infinite type, or the tensor product of a UHF algebra of infinite type and $\mathcal{O}_{\infty}$, then the conjugation action $\mathrm{Aut}(A)…

We show that a $C^*$-algebra $A$ is nuclear iff there is a constant $K$ and $\alpha<3$ such that, for any bounded homomorphism $u\colon A \to B(H)$, there is an isomorphism $\xi\colon H\to H$ satisfying $\|\xi^{-1}\|\|\xi\| \le…

We construct a simple, separable, unital, and nuclear C*-algebra with weakly unperforated K_0-group which does not absorb the Jiang-Su algebra Z tensorially. As a result, we obtain a stably finite counter-example to Elliott's classification…

We show that unital simple C*-algebras with tracial topological rank zero which are locally approximated by subhomogeneous C^-algebras can be classified by their ordered $K$-theory. We apply this classification result to show that certain…

We prove that the isomorphism problem for separable nuclear C*-algebras is complete in the class of orbit equivalence relations. In fact, already the isomorphism of simple, separable AI C*-algebras is a complete orbit equivalence relation.…

Let $A$ be a simple separable unital locally approximately subhomogeneous C*-algebra (locally ASH algebra). It is shown that $A\otimes Q$ can be tracially approximated by unital Elliott-Thomsen algebras with trivial $\textrm{K}_1$-group,…

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.

Starting from Kirchberg's theorems announced in 1994, namely O_2 tensor A is isomorphic to O_2 for separable unital nuclear simple A and O_infinity tensor A is isomorphic to A if in addition A is purely infinite, we prove that…

We prove that the automorphisms of any separable C*-algebra that does not have continuous trace are not classifiable by countable structures up to unitary equivalence. This implies a dichotomy for the Borel complexity of the relation of…

Examples of simple, separable, unital, purely infinite $C^*$--algebras are constructed, including: (1) some that are not approximately divisible; (2) those that arise as crossed products of any of a certain class of $C^*$--algebras by any…

Glimm's theorem says that a UHF algebra is almost embedded in a separable $C^*$-algebra not of type I. Applying his methods we obtain a covariant version of his result; a UHF algebra with a product type automorphism is covariantly embedded…

We study the automorphism group of a unital, simple, $\mathcal{Z}$-stable $C^{*}$-algebra. In this paper, we generalize the results by the authors in \cite{pr_auto} to $\mathcal{Z}$-stable $C^{*}$-algebras $\mathfrak{A}$ such that…

Let X be an infinite compact metric space with finite covering dimension and let h be a minimal homeomorphism of X. Let A be the associated crossed product C*-algebra. We show that A has tracial rank zero whenever the image of K_0 (A) in…

We provide some background on the category of classifiable $\mathrm{C}^*$-algebras, whose objects are infinite-dimensional, simple, separable, unital $\mathrm{C}^*$-algebras that have finite nuclear dimension and satisfy the universal…

In contrast to C*-algebras, distinct C*-norms on the algebraic tensor product of two W*-algebras produce isomorphic W*-tensor products

Let $A$ and $C$ be two unital simple C*-algebas with tracial rank zero. Suppose that $C$ is amenable and satisfies the Universal Coefficient Theorem. Denote by ${{KK}}_e(C,A)^{++}$ the set of those $\kappa$ for which…

For unital $C^*$-algebras $A$ and $B$, we completely characterize the isometric ($*$-) automorphisms of their Banach space projective tensor product $A\otimes^\gamma B$. This leads to the characterization of inner and outer isometric…

Let $A$ be a unital simple separable C*-algebra satisfying the UCT. Assume that $\mathrm{dr}(A)<+\infty$, $A$ is Jiang-Su stable, and $\mathrm{K}_0(A)\otimes \mathbb{Q}\cong \mathbb{Q}$. Then $A$ is an ASH algebra (indeed, $A$ is a…