Equivalence of Fell bundles over groups

Abadie, Fernando; Ferraro, Damián

doi:10.7900/jot.2018feb02.2211

Cited by 4 publications

(2 citation statements)

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“…Proof. The same proof given in [1] for groups extends to inverse semigroups. Using Lemma 5.2 we may now see A ⊗ min B and A ⊗ max B as Fell bundles over S whose bundle structure comes as a continuous extension of that of the "algebraic" bundle A ⊙ B = (A s ⊙ B) s∈S .…”

Section: Tensor Products Of Fell Bundlesmentioning

confidence: 66%

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Approximation properties of Fell bundles over inverse semigroups and non-Hausdorff groupoids

Buss¹,

Martínez²

2023

Preprint

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In this paper we study the nuclearity and weak containment property of reduced cross-sectional C * -algebras of Fell bundles over inverse semigroups. In order to develop the theory, we first prove an analogue of Fell's absorption trick in the context of Fell bundles over inverse semigroups. In parallel, the approximation property of Exel can be reformulated in this context, and Fell's absorption trick can be used to prove that the approximation property, as defined here, implies that the full and reduced cross-sectional C * -algebras are isomorphic via the left regular representation, i.e., the Fell bundle has the weak containment property.We then use this machinery to prove that a Fell bundle with the approximation property and nuclear unit fiber has a nuclear cross-sectional C * -algebra. This result gives nuclearity of a large class of C * -algebras, as, remarkably, all the machinery in this paper works for étale non-Hausdorff groupoids just as well.

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Section: Tensor Products Of Fell Bundlesmentioning

confidence: 66%

“…It is, however, not yet known whether the weak containment property for A implies its approximation property. 1 Lastly, Kranz recently [26] generalized the notion of approximation property so as to cover Fell bundles over (second countable) locally compact Hausdorff étale groupoids, and derived some of the expected results.…”

Section: Introductionmentioning

confidence: 99%

Approximation properties of Fell bundles over inverse semigroups and non-Hausdorff groupoids

Buss¹,

Martínez²

2023

Preprint

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Strong equivalence of graded algebras

Abadie,

Dokuchaev,

Exel

2024

Journal of Algebra

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Stone duality and quasi‐orbit spaces for generalised C∗‐inclusions

Kwaśniewski

Meyer

2020

Proc. London Math. Soc.

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Let A be a C *-subalgebra of the multiplier algebra M(B) of a C *-algebra B. Exploiting the duality between sober spaces and spatial locales, and the adjunction between restriction and induction for ideals in A and B, we identify conditions that allow to define a quasi-orbit space and a quasi-orbit map for A ⊆ M(B). These objects generalise classical notions for group actions. We characterise when the quasi-orbit space is an open quotient of the primitive ideal space of A and when the quasi-orbit map is open and surjective. We apply these results to cross-section C *-algebras of Fell bundles over locally compact groups, regular C *-inclusions, tensor products, relative Cuntz-Pimsner algebras and crossed products for actions of locally compact Hausdorff groupoids and quantum groups.

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Equivalence of Fell bundles over groups

Cited by 4 publications

References 3 publications

Approximation properties of Fell bundles over inverse semigroups and non-Hausdorff groupoids

Approximation properties of Fell bundles over inverse semigroups and non-Hausdorff groupoids

Strong equivalence of graded algebras

Stone duality and quasi‐orbit spaces for generalised C∗‐inclusions

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