# š-Stable ASH Algebras

@article{Toms2008StableAA, title={š-Stable ASH Algebras}, author={Andrew S. Toms and Wilhelm Winter}, journal={Canadian Journal of Mathematics}, year={2008}, volume={60}, pages={703 - 720} }

Abstract The JiangāSu algebra $Z$ has come to prominence in the classification program for nuclear ${{C}^{*}}$ -algebras of late, due primarily to the fact that Elliottās classification conjecture in its strongest form predicts that all simple, separable, and nuclear ${{C}^{*}}$ -algebras with unperforated $\text{K}$ -theory will absorb $Z$ tensorially, i.e., will be $Z$ -stable. There exist counterexamples which suggest that the conjecture will only hold for simple, nuclear, separable and $Zā¦Ā

## 28 Citations

### A stably finite analogue of the Cuntz algebra O2

- Mathematics
- 2011

The Elliott Programme seeks classification of simple, separable, nuclear $C^*$-algebras via a functor based on $K$-theory. There are a handful of $C^*$-algebras, including the Cuntz algebrasā¦

### Recasting the Elliott conjecture

- Mathematics
- 2006

Let A be a simple, unital, finite, and exact C*-algebra which absorbs the JiangāSu algebra $${\mathcal{Z}}$$ tensorially. We prove that the Cuntz semigroup of A admits a complete order embedding intoā¦

### Nuclear dimension and $\mathcal{Z}$-stability of pure Cā-algebras

- Mathematics
- 2012

In this article I study a number of topological and algebraic dimension type properties of simple Cā-algebras and their interplay. In particular, a simple Cā-algebra is defined to be (tracially)ā¦

### Hausdorffified algebraic K1-groups and invariants for Cā-algebras with the ideal property

- MathematicsAnnals of K-Theory
- 2020

A $C^*$-algebra $A$ is said to have the ideal property if each closed two-sided ideal of $A$ is generated by the projections inside the ideal, as a closed two sided ideal. $C^*$-algebras with theā¦

### Ęµ-Stability of Crossed Products by Strongly Outer Actions II

- Mathematics
- 2014

We consider a crossed product of a unital simple separable nuclear stably finite $\cal Z$-stable $C^*$-algebra $A$ by a strongly outer cocycle action of a discrete countable amenable group $\Gamma$.ā¦

### Decomposition rank and $\mathcal{Z}$ -stability

- Mathematics
- 2009

AbstractWe show that separable, simple, nonelementary, unital C*-algebras with finite decomposition rank absorb the JiangāSu algebra
$\mathcal{Z}$
tensorially. This has a number of consequences forā¦

### Nuclear dimension and $$\mathcal Z$$Z-stability

- Mathematics
- 2015

Simple, separable, unital, monotracial and nuclear $$\mathrm {C}^{*}$$Cā-algebras are shown to have finite nuclear dimension whenever they absorb the JiangāSu algebra $$\mathcal {Z}$$Z tensorially.ā¦

### D-stable C*-algebras, the ideal property and real rank zero

- Mathematics
- 2009

Let D be a strongly self-absorbing, K1-injective C Ā¤ -algebra (e.g., the Jiang-Su algebra Z and O1). We characterize, in particular, when A Ā D has the ideal property, where A is a separable, purelyā¦

### Rokhlin Dimension and C*-Dynamics

- Mathematics
- 2012

We develop the concept of Rokhlin dimension for integer and for finite group actions on C*-algebras. Our notion generalizes the so-called Rokhlin property, which can be thought of as Rokhlinā¦

### The Cuntz semigroup, the Elliott conjecture, and dimension functions on C*-algebras

- Mathematics
- 2006

Abstract We prove that the Cuntz semigroup is recovered functorially from the Elliott invariant for a large class of C*-algebras. In particular, our results apply to the largest class of simpleā¦

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