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

We prove that if Λ is a row‐finite k‐graph with no sources, then the associated C*‐algebra is simple if and only if Λ is cofinal and satisfies Kumjian and Pask's aperiodicity condition, known as…
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Zappa-Sz\'ep products of semigroups and their C*-algebras

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

For bi-Hilbertian $A$-bimodules, in the sense of Kajiwara--Pinzari--Watatani, we construct a Kasparov module representing the extension class defining the Cuntz--Pimsner algebra. The construction…
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Groupoid algebras as Cuntz-Pimsner algebras

We show that if $G$ is a second countable locally compact Hausdorff \'etale groupoid carrying a suitable cocycle $c:G\to\mathbb{Z}$, then the reduced $C^*$-algebra of $G$ can be realised naturally as…
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Simplicity of C*-algebras associated to row-finite locally convex higher-rank graphs

In a previous work, the authors showed that the C*-algebra C*(Λ) of a row-finite higher-rank graph Λ with no sources is simple if and only if Λ is both cofinal and aperiodic. In this paper, we…
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A new look at crossed product correspondences and associated C*-algebras

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

Abstract 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…
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Coactions on Cuntz-Pimsner Algebras

We investigate how a correspondence coaction gives rise to a coaction on the associated Cuntz-Pimsner algebra. We apply this to recover a recent result of Hao and Ng concerning Cuntz-Pimsner algebras…
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Zappa–Szép product groupoids and $$C^*$$C∗-blends

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…
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Reconstructing directed graphs from generalized gauge actions on their Toeplitz algebras

Abstract We show how to reconstruct a finite directed graph E from its Toeplitz algebra, its gauge action, and the canonical finite-dimensional abelian subalgebra generated by the vertex projections.…
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