We produce a complete descrption of the lattice of gauge-invariant ideals in C * (Λ) for a finitely aligned k-graph Λ. We provide a condition on Λ under which every ideal is gauge-invariant. We give conditions on Λ under which C * (Λ) satisfies the hypotheses of the Kirchberg-Phillips classification theorem.
General Information SATEN 1 is an object-oriented web-based extraction and belief revision engine. It runs on any computer via a Java 1.1 enabled browser such as Netscape 4. SATEN performs belief revision based on the AGM approach (Alchourrón et al 85). The extraction and belief revision reasoning engines operate on a user specified ranking of information.… (More)
This paper is comprised of two related parts. First we discuss which k-graph algebras have faithful traces. We characterise the existence of a faithful semifinite lower-semicontinuous gauge-invariant trace on C * (Λ) in terms of the existence of a faithful graph trace on Λ. Second, for k-graphs with faithful gauge invariant trace, we construct a smooth (k,… (More)
We define the relative Cuntz-Krieger algebras associated to finitely aligned higher-rank graphs. We prove versions of the gauge-invariant uniqueness theorem and the Cuntz-Krieger uniqueness theorem for relative Cuntz-Krieger algebras.
Let X be a product system over a quasi-lattice ordered group. Under mild hypotheses, we associate to X a C *-algebra which is co-universal for injective Nica covariant Toeplitz representations of X which preserve the gauge coaction. Under appropriate amenability criteria, this co-universal C *-algebra coincides with the Cuntz-Nica-Pimsner algebra introduced… (More)
In [PRen] we constructed smooth (1, ∞)-summable semfinite spectral triples for graph algebras with a faithful trace, and in [PRS] we constructed (k, ∞)-summable semifinite spectral triples for k-graph algebras. In this paper we identify classes of graphs and k-graphs which satisfy a version of Connes' conditions for noncommutative manifolds.
We develop notions of a representation of a topological graph E and of a covariant representation of a topological graph E which do not require the machinery of C *-correspondences and Cuntz– Pimsner algebras. We show that the C *-algebra generated by a universal representation of E is isomorphic to the Toeplitz algebra of Katsura's topological-graph… (More)
We show that if E is an equivalence of upper semicontinu-ous Fell bundles B and C over groupoids, then there is a linking bundle L(E) over the linking groupoid L such that the full cross-sectional algebra of L(E) contains those of B and C as complementary full corners, and likewise for reduced cross-sectional algebras. We show how our results generalise to… (More)
Let E be a row-finite directed graph. We prove that there exists a C *-algebra C * min (E) with the following co-universal property: given any C *-algebra B generated by a Toeplitz-Cuntz-Krieger E-family in which all the vertex projections are nonzero, there is a canonical homomorphism from B onto C * min (E). We also identify when a homomorphism from B to… (More)