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

@article{Armstrong2017ProductsystemMF, title={Product-system models for twisted C⁎-algebras of topological higher-rank graphs}, author={Becky Armstrong and Nathan Brownlowe}, journal={Journal of Mathematical Analysis and Applications}, year={2017} }

## 3 Citations

### Simplicity of twisted C*-algebras of Deaconu--Renault groupoids

- Mathematics
- 2021

We consider Deaconu–Renault groupoids associated to actions of finite-rank free abelian monoids by local homeomorphisms of locally compact Hausdorff spaces. We study simplicity of the twisted…

### Iterating the Cuntz-Nica-Pimsner construction for compactly aligned product systems

- Mathematics
- 2017

In this article we study how decompositions of a quasi-lattice ordered group $(G,P)$ relate to decompositions of the Nica-Toeplitz algebra $\mathcal{NT}_\mathbf{X}$ and Cuntz-Nica-Pimsner algebra…

## References

SHOWING 1-10 OF 44 REFERENCES

### Product systems of graphs and the Toeplitz algebras of higher-rank graphs | NOVA. The University of Newcastle's Digital Repository

- Mathematics
- 2003

There has recently been much interest in the C � -algebras of directed graphs. Here we consider product systems E of directed graphs over semigroups and associated C � -algebras C � (E) and T C � (E)…

### 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…

### On twisted higher-rank graph C*-algebras

- Mathematics
- 2011

We define the categorical cohomology of a k-graphand show that the first three terms in this cohomology are isomorphic to the corresponding terms in the cohomology defined in our previous paper. This…

### 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…

### C*-algebras associated to product systems of hilbert bimodules

- Mathematics
- 2007

Let (G,P) be a quasi-lattice ordered group and let X be a compactly aligned product system over P of Hilbert bimodules. Under mild hypotheses we associate to X a C*-algebra which we call the…

### 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…

### Co-universal C*-algebras associated to generalised graphs

- Mathematics
- 2010

We introduce P-graphs, which are generalisations of directed graphs in which paths have a degree in a semigroup P rather than a length in ℕ. We focus on semigroups P arising as part of a…

### 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…