## 24 Citations

### Simplicity of twisted C*-algebras of higher-rank graphs and crossed products by quasifree actions

- Mathematics
- 2014

We characterise simplicity of twisted C*-algebras of row-finite k-graphs with no sources. We show that each 2-cocycle on a cofinal k-graph determines a canonical second-cohomology class for the…

### SIMPLICITY OF TWISTED C*-ALGEBRAS OF TOPOLOGICAL HIGHER-RANK GRAPHS

- MathematicsBulletin of the Australian Mathematical Society
- 2020

In a recent series of papers, Kumjian, Pask and Sims [2–5] have investigated the effect of ‘twisting’ C∗-algebras associated to higher-rank graphs using a categorical 2-cocycle on the graph. This…

### GRAPHS AND CROSSED PRODUCTS BY QUASIFREE ACTIONS

- Mathematics
- 2014

We characterise simplicity of twisted C � -algebras of row-finite k-graphs with no sources. We show that each 2-cocycle on a cofinal k-graph determines a canonical second-cohomology class for the…

### Twisted $C^*$-algebras associated to finitely aligned higher-rank graphs

- MathematicsDocumenta Mathematica
- 2014

We introduce twisted relative Cuntz-Krieger algebras associated to finitely aligned higher-rank graphs and give a comprehensive treatment of their fundamental structural properties. We establish…

### Product-system models for twisted C⁎-algebras of topological higher-rank graphs

- MathematicsJournal of Mathematical Analysis and Applications
- 2018

### 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…

### K-theory and homotopies of twists on ample groupoids

- MathematicsJournal of Noncommutative Geometry
- 2021

This paper investigates the K-theory of twisted groupoid C*-algebras. It is shown that a homotopy of twists on an ample groupoid satisfying the Baum–Connes conjecture with coefficients gives rise to…

### K-theory and homotopies of 2-cocycles on higher-rank graphs

- Mathematics
- 2015

This paper continues our investigation into the question of when a homotopy of 2-cocycles on a locally compact Hausdorff groupoid gives rise to an isomorphism of the K-theory groups of the twisted…

## References

SHOWING 1-10 OF 30 REFERENCES

### Skew-products of higher-rank graphs and crossed products by semigroups

- Mathematics
- 2012

We consider a free action of an Ore semigroup on a higher-rank graph, and the induced action by endomorphisms of the C∗-algebra of the graph. We show that the crossed product by this action is stably…

### On the K-theory of higher rank graph C ∗ -algebras

- Mathematics
- 2004

Given a row-finite k-graph Λ with no sources we investigate the K-theory of the higher rank graph C ∗ -algebra, C ∗ (Λ). When k = 2 we are able to give explicit formulae to calculate the K-groups of…

### HOMOLOGY FOR HIGHER-RANK GRAPHS AND TWISTED

- Mathematics
- 2011

We introduce a homology theory for k-graphs and explore its fundamental properties. We establish connections with algebraic topology by showing that the homol- ogy of a k-graph coincides with the…

### 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…

### On higher rank graph C ∗ -algebras

- Mathematics
- 2000

Given a row-finite k-graph Λ with no sources we investigate the K-theory of the higher rank graph C *-algebra, C * (Λ). When k = 2 we are able to give explicit formulae to calculate the K-groups of C…

### Affine buildings, tiling systems and higher rank Cuntz-Krieger algebras

- Mathematics
- 1999

To an $r$-dimensional subshift of finite type satisfying certain special properties we associate a $C^*$-algebra $\cA$. This algebra is a higher rank version of a Cuntz-Krieger algebra. In…

### The K-Theory of Heegaard-Type Quantum 3-Spheres

- Mathematics
- 2004

We use a Heegaard splitting of the topological 3-sphere as a guiding principle to construct a family of its noncommutative deformations. The main technical point is an identification of the universal…

### A Locally Trivial Quantum Hopf Fibration

- Mathematics
- 2001

Abstract
The irreducible *-representations of the polynomial algebra
$\mathcal{O}(S^{3}_{pq})$
of the quantum3-sphere introduced by Calow and Matthes are classified. The K-groups of its universal…

### Higher-Rank Graph C *-Algebras: An Inverse Semigroup and Groupoid Approach

- Mathematics
- 2004

AbstractWe provide inverse semigroup and groupoid models for the Toeplitz and Cuntz-Krieger algebras of finitely aligned higher-rank graphs. Using these models, we prove a
uniqueness theorem for the…