David I Robertson

Simplicity of C*-algebras associated to higher-rank graphs

We prove that ifis a row-finite k-graph with no sources, then the associated C � -algebra is simple if and only ifis cofinal and satisfies Kumjian and Pasks aperiodicity condition, known as Condition (A). We prove that the aperiodicity condition is equivalent to a suitably modified version of Robertson and Stegers original nonperiodicity condition (H3) which in particular involves only finite paths. We also characterise both cofinality and aperiodicity ofin terms of ideals in C � (�).

The extension class and KMS states for Cuntz–Pimsner algebras of some bi-Hilbertian bimodules

For bi-Hilbertian

Groupoid Fell bundles for product systems over quasi-lattice ordered groups

A

Zappa-Szép product groupoids and C∗-blends

-bimodules, in the sense of Kajiwara--Pinzari--Watatani, we construct a Kasparov module representing the extension class defining the Cuntz--Pimsner algebra. The construction utilises a singular expectation which is defined using the

SIMPLICITY OF C ∗ -ALGEBRAS ASSOCIATED TO ROW-FINITE LOCALLY CONVEX HIGHER-RANK GRAPHS

C^*

Zappa–Szép products of semigroups and their C*-algebras

-module version of the Jones index for bi-Hilbertian bimodules. The Jones index data also determines a novel quasi-free dynamics and KMS states on these Cuntz--Pimsner algebras.

Functoriality of Cuntz–Pimsner correspondence maps

Consider a product system over the positive cone of a quasi-lattice ordered group. We construct a Fell bundle over an associated groupoid so that the cross-sectional algebra of the bundle is isomorphic to the Nica-Toeplitz algebra of the product system. Under the additional hypothesis that the left actions in the product system are implemented by injective homomorphisms, we show that the cross-sectional algebra of the restriction of the bundle to a natural boundary subgroupoid coincides with the Cuntz-Nica-Pimsner algebra of the product system. We apply these results to improve on existing sufficient conditions for nuclearity of the Nica-Toeplitz algebra and the Cuntz-Nica-Pimsner algebra, and for the Cuntz-Nica-Pimsner algebra to coincide with its co-universal quotient.

A new look at crossed product correspondences and associated C*-algebras

We study the external and internal Zappa–Szép product of topological groupoids. We show that under natural continuity assumptions the Zappa–Szép product groupoid is étale if and only if the individual groupoids are étale. In our main result we show that the

Groupoid algebras as Cuntz-Pimsner algebras

C^*