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Unconditional integrability for dual actions

AbstractThe dual action of a locally compact abelian group, in the context of C*-algebraic bundles, is shown to satisfy an integrability property, similar to Rieffel's proper actions. The tools...

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Exact groups and Fell bundles

Abstract. Kirchberg and Wasserman's Theorem, according to which a group is exact if and only if its reduced C*-algebra is exact, is extended to the context of Fell bundles.

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Partial Dynamical Systems and the KMS Condition

Abstract: Given a countably infinite 0–1 matrix A without identically zero rows, let 𝒪A be the Cuntz–Krieger algebra recently introduced by the authors and 𝒯A be the Toeplitz extension of 𝒪A, once the...

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KMS States for generalized Gauge actions on Cuntz-Krieger algebras

Abstract.Given a zero-one matrix A we consider certain one-parameter groups of automorphisms of the Cuntz-Krieger algebra \( {\user1{\mathcal{O}}}_{A} \), generalizing the usual gauge group, and...

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On the Singularities of the Exponential Map in Infinite Dimensional...

AbstractUsing symplectic techniques and spectral analysis of smooth paths of self-adjoint operators, we characterize the set of conjugate instants along a geodesic in an infinite dimensional Riemannian...

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The Crossed Product by a Partial Endomorphism

Abstract.Given a closed ideal I in a C*-algebra A, an ideal J (not necessarily closed) in I , a *-homomorphism α : A→ M(I ) and a map L : J→ A with some properties, based on earlier works of Pimsner...

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Inverse semigroups and combinatorial C*-algebras

Abstract.We describe a special class of representations of an inverse semigroup S on Hilbert's space which we term tight. These representations are supported on a subset of the spectrum of the...

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The tiling C*-algebra viewed as a tight inverse semigroup algebra

AbstractWe realize Kellendonk’s C*-algebra of an aperiodic tiling as the tight C*-algebra of the inverse semigroup associated to the tiling, thus providing further evidence that the tight C*-algebra is...

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Inverse semigroup actions as groupoid actions

AbstractTo an inverse semigroup, we associate an étale groupoid such that its actions on topological spaces are equivalent to actions of the inverse semigroup. Both the object and the arrow space of...

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Invertibility in Groupoid C *-algebras

AbstractGiven a second-countable, Hausdorff, étale, amenable groupoid \(\mathcal{G}\) with compact unit space, we show that an element a in \(C^{\star}(\mathcal{G})\) is invertible if and only if...

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The tight groupoid of an inverse semigroup

AbstractIn this work we present algebraic conditions on an inverse semigroup \(\mathcal {S}\) (with zero) which imply that its associated tight groupoid \(\mathcal {G}_\mathrm{tight}(\mathcal {S})\)...

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Reduced C*-algebras of Fell bundles over inverse semigroups

AbstractWe construct a weak conditional expectation from the section C*-algebra of a Fell bundle over a unital inverse semigroup to its unit fibre. We use this to define the reduced C*-algebra of the...

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Tight and Cover-to-Join Representations of Semilattices and Inverse Semigroups

AbstractWe discuss the relationship between tight and cover-to-join representations of semilattices and inverse semigroups, showing that a slight extension of the former, together with an appropriate...

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Examples and Open Questions

AbstractAs we have seen, the notion of smooth normalizers is a central piece of our strategy for dealing with regular inclusions. In this section we would like to exhibit a light inclusion of abelian...

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Inclusions

AbstractOne of the most basic aspects of our techniques, to be developed in this and the following section, is the study of the algebraic relationship between ideals in a C*-algebra A, on the one hand,...

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Groupoids

AbstractSo far our standing assumptions have always involved a fixed inclusion of C*-algebras. From this point on we will instead concentrate our attention on groupoids which will in due time lead to a...

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Characterizing Groupoid C*-algebras of Non-Hausdorff Étale Groupoids

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Appendix: Isotropy Projection

AbstractOur goal in this section is to prove (5.9) below, which is a basic result in the theory of twisted groupoid C*-algebras. We have been unable to locate this result in the literature in the...

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Introduction

AbstractIn their landmark paper, Feldman and Moore gave methods for describing certain von Neumann algebras using twisted measured equivalence relations arising from a Cartan MASA. Their result may be...

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A remark on contracting inverse semigroups

AbstractA semi-lattice is said to be tree-like when any two of its elements are either orthogonal or comparable. Given an inverse semigroup \(\mathcal{S}\) whose idempotent semi-lattice is tree-like,...

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