## 12 Citations

### Nuclear dimension of extensions of $\mathcal{O}_\infty$-stable algebras.

- Mathematics
- 2020

We obtain an improved upper bound for the nuclear dimension of extensions of $\mathcal{O}_\infty$-stable $\rm{C}^*$-algebras. In particular, we prove that the nuclear dimension of a full extension of…

### ALGEBRAS HAVE NUCLEAR DIMENSION ONE

- Mathematics
- 2021

. We prove that unital extensions of Kirchberg algebras by separable stable AF algebras have nuclear dimension one. The title follows.

### The Cuntz–Toeplitz algebras have nuclear dimension one

- MathematicsJournal of Functional Analysis
- 2020

### Sturmian subshifts and their C*-algebras

- Mathematics
- 2021

This paper investigates the structure of C∗-algebras built from one-sided Sturmian subshifts. They are parametrised by irrationals in the unit interval and built from a local homeomorphism associated…

### The Rokhlin property vs. Rokhlin dimension 1 on unital Kirchberg algebras

- Mathematics
- 2013

We investigate symmetries on unital Kirchberg algebras with respect to the Rokhlin property and finite Rokhlin dimension. In stark contrast to the restrictiveness of the Rokhlin property, every such…

### KMS States on Generalised Bunce–Deddens Algebras and their Toeplitz Extensions

- Mathematics
- 2015

We study the generalised Bunce–Deddens algebras and their Toeplitz extensions constructed by Kribs and Solel from a directed graph and a sequence $$\omega $$ω of positive integers. We describe both…

## References

SHOWING 1-10 OF 37 REFERENCES

### Graph C*-Algebras with Real Rank Zero

- Mathematics
- 2002

Given a row-finite directed graph E, a universal C*-algebra C*(E) generated by a family of partial isometries and projections subject to the relations determined by E is associated to the graph E.…

### Stability of C^*-algebras associated to graphs

- Mathematics
- 2002

We characterize stability of graph C*-algebras by giving five conditions equivalent to their stability. We also show that if G is a graph with no sources, then C*(G) is stable if and only if each…

### Ideals in Graph Algebras

- Mathematics
- 2012

We show that the graph construction used to prove that a gauge-invariant ideal of a graph C ∗ -algebra is isomorphic to a graph C ∗ -algebra, and also used to prove that a graded ideal of a Leavitt…

### Nuclear dimension and -stability of pure C ∗ -algebras

- Mathematics
- 2010

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)…

### Purely Infinite Cuntz–Krieger Algebras of Directed Graphs

- Mathematics
- 2003

For arbitrary infinite directed graphs E, the characterisation of the (not necessarily simple) Cuntz–Krieger algebras C*(E) which are purely infinite in the sense of Kirchberg–Rørdam is given. It is…

### A Class of Limit Algebras Associated with Directed Graphs

- MathematicsJournal of the Australian Mathematical Society
- 2007

Abstract Every directed graph defines a Hilbert space and a family of weighted shifts that act on the space. We identify a natural notion of periodicity for such shifts and study their C* -algebras.…

### The Toeplitz algebra of a Hilbert bimodule

- Mathematics
- 1998

Suppose a C*-algebra A acts by adjointable operators on a Hilbert A-module X. Pimsner constructed a C*-algebra O_X which includes, for particular choices of X, crossed products of A by Z, the Cuntz…

### Decomposition rank of UHF-absorbing c* -algebras

- Mathematics
- 2013

Let A be a unital separable simple C*-algebra with a unique tracial state. We prove that if A is nuclear and quasidiagonal, then A tensored with the universal UHF-algebra has decomposition rank at…

### THE C -ALGEBRAS OF ROW-FINITE GRAPHS

- Mathematics
- 2000

NSKI Abstract. We prove versions of the fundamental theorems about Cuntz-Krieger algebras for the C -algebras of row-finite graphs: directed graphs in which each vertex emits at most finitely many…