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

  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},

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

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

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



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

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)

Homology for higher-rank graphs and twisted C*-algebras

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

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

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

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

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


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

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

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