Related papers: A tracially AF algebra which is not $\mathcal Z$-a…

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 study properties of the central sequence algebra of a C*-algebra, and we present an alternative approach to a recent result of Matui and Sato. They prove that every unital separable simple nuclear C*-algebra, whose trace simplex 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…

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…

A classification theorem is obtained for a class of unital simple separable amenable Z-stable C*-algebras which exhausts all possible values of the Elliott invariant for unital stably finite simple separable amenable Z-stable C*-algebras.…

Let $G$ be an inductive limit of finite cyclic groups and let $A$ be a unital simple projectionless C*-algebra with $K_1(A) \cong G$ and with a unique tracial state, as constructed based on dimension drop algebras by Jiang and Su. First, we…

Say that a separable, unital C*-algebra D is strongly self-absorbing if there exists an isomorphism $\phi: D \to D \otimes D$ such that $\phi$ and $id_D \otimes 1_D$ are approximately unitarily equivalent $*$-homomorphisms. We study this…

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…

Let $A$ be a unital AH-algebra and let $\alpha\in Aut(A)$ be an automorphism. A necessary condition for $A\rtimes_{\alpha}\Z$ being embedded into a unital simple AF-algebra is the existence of a faithful tracial state. If in addition, there…

We show that every separable simple tracially approximately divisible $C^*$-algebra has strict comparison, is either purely infinite, or has stable rank one. As a consequence, we show that every (non-unital) finite simple ${\cal Z}$-stable…

Let $X$ be a compact metric space and let $\Lambda$ be a $\Z^k$ ($k\ge 1$) action on $X.$ We give a solution to a version of Voiculescu's problem of AF-embedding: The crossed product $C(X)\rtimes_{\Lambda}\Z^k$ can be embedded into a unital…

For projectionless C*-algebras absorbing the Jiang-Su algebra tensorially, we study a kind of the Rohlin property for autmorphisms. We show that the crossed products obtained by automorphisms with this Rohlin property also absorb the…

We give a classification theorem for unital separable simple nuclear $C^*$-algebras with tracial topological rank zero which satisfy the Universal Coefficient Theorem. We prove that if $A$ and $B$ are two such $C^*$-algebras and $$ (K_0(A),…

We give a number of new characterizations of the Jiang-Su algebra Z, both intrinsic and extrinsic, in terms of C*-algebraic, dynamical, topological and K-theoretic conditions. Along the way we study divisibility properties of C*-algebras,…

We introduce and study a notion of Rokhlin property for an inclusion of unital $C^*$-algebras which could have no projections like the Jiang-Su algebra. We also introduce a notion of approximate representability and show a duality between…

We prove the title. This characterizes the Jiang-Su algebra Z as the uniquely determined initial object in the category of strongly self-absorbing C*-algebras.

We give an example of a unital C*-algebra $\mathbf{A}$ with a computable presentation and for which neither $K_0(\mathbf{A})$ nor $K_1(\mathbf{A})$ has a computable presentation.

Let A be a unital AF-algebra (simple or non-simple) and let \alpha be an automorphism of A. Suppose that \alpha has certain Rokhlin property and A is \alpha-simple. Suppose also that there is an integer J\geq1 such that…

We show that a tracial state on a unital C*-algebra admits a Haar unitary if and only if it is diffuse, if and only if it does not dominate a tracial functional that factors through a finite-dimensional quotient. It follows that a unital…

We introduce stabilised property Gamma, a C*-algebraic variant of property Gamma which is invariant under stable isomorphism. We then show that simple separable nuclear C*-algebras with stabilised property Gamma and $\mathrm{Cu}(A) \cong…