## 37 Citations

### All classifiable Kirchberg algebras are C∗-algebras of ample groupoids

- MathematicsExpositiones Mathematicae
- 2020

### 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…

### 𝐶*-algebras and their nuclear dimension

- MathematicsMexican Mathematicians in the World
- 2021

We review the notion of nuclear dimension for
C
∗
\mathrm {C}^*
-algebras introduced by Winter and Zacharias. We explain why it is a non-commutative version of topological…

### Irreducibility and monicity for representations of $k$-graph $C^*$-algebras

- Mathematics
- 2021

The representations of a k-graph C∗-algebra C∗(Λ) which arise from Λ-semibranching function systems are closely linked to the dynamics of the k-graph Λ. In this paper, we undertake a systematic…

### K-theory for real k-graph C∗-algebras

- MathematicsAnnals of K-Theory
- 2022

. We initiate the study of real C ∗ -algebras associated to higher-rank graphs Λ, with a focus on their K -theory. Following Kasparov and Evans, we identify a spectral sequence which computes the CR…

### Homotopy of product systems and K-theory of Cuntz-Nica-Pimsner algebras

- MathematicsIndiana University Mathematics Journal
- 2022

We introduce the notion of a homotopy of product systems, and show that the Cuntz-Nica-Pimsner algebras of homotopic product systems over N^k have isomorphic K-theory. As an application, we give a…

### Rohklin dimension for C*-correspondences

- Mathematics
- 2015

We extend the notion of Rokhlin dimension from topological dynamical systems to $C^*$-correspondences. We show that in the presence of finite Rokhlin dimension and a mild quasidiagonal-like condition…

## References

SHOWING 1-10 OF 31 REFERENCES

### 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…

### Nuclear dimension and Z -stability

- Mathematics
- 2015

Simple, separable, unital, monotracial and nuclear C ∗ -algebras are shown to have ﬁnite nuclear dimension whenever they absorb the Jiang–Su algebra Z tensorially. This completes the proof of the…

### 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…

### 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.…

### Minimal Dynamics and K-Theoretic Rigidity: Elliott’s Conjecture

- Mathematics
- 2009

Let X be a compact infinite metric space of finite covering dimension and α : X → X a minimal homeomorphism. We prove that the crossed product $${\mathcal{C}(X) \rtimes_\alpha \mathbb{Z}}$$ absorbs…

### 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)…

### Higher Rank Graph C-Algebras

- Mathematics
- 2000

Building on recent work of Robertson and Steger, we associate a C{algebra to a combinatorial object which may be thought of as a higher rank graph. This C{algebra is shown to be isomorphic to that of…