Groupoids Associated with Endomorphisms

Deaconu, Valentin

doi:10.2307/2154972

Cited by 63 publications

(112 citation statements)

References 0 publications

Supporting

Mentioning

110

Contrasting

Order By: Relevance

“…We mention one typical case: Example 3.16. Let H be the groupoid associated to a self-covering σ : X → X of a compact space X as in [9]. The canonical Z-valued cocycle π : H → Z on it clearly has the properties needed to define a Z-grading on H. The subgroupoid G := π −1 (0) is the groupoid that describes the equivalence relation generated by…”

Section: Examples: Group Actions and Actions On Spacesmentioning

confidence: 99%

Inverse semigroup actions on groupoids

Buss¹,

Meyer²

2017

Rocky Mountain J. Math.

View full text Add to dashboard Cite

We define inverse semigroup actions on topological groupoids by partial equivalences. From such actions, we construct saturated Fell bundles over inverse semigroups and non-Hausdorff \'etale groupoids. We interpret these as actions on C*-algebras by Hilbert bimodules and describe the section algebras of these Fell bundles. Our constructions give saturated Fell bundles over non-Hausdorff \'etale groupoids that model actions on locally Hausdorff spaces. We show that these Fell bundles are usually not Morita equivalent to an action by automorphisms. That is, the Packer-Raeburn Stabilisation Trick does not generalise to non-Hausdorff groupoids.Comment: 59 pages. Proofreading with minor changes. Version accepted for publication at Rocky Mountain Journa

show abstract

Section: Examples: Group Actions and Actions On Spacesmentioning

confidence: 99%

Inverse semigroup actions on groupoids

Buss¹,

Meyer²

2017

Rocky Mountain J. Math.

View full text Add to dashboard Cite

show abstract

“…Next, we show that Γ can be seen as a Renault-Deaconu groupoid [21,11,22]. For that we define, for each n ∈ N with n ≥ 1, T (n) = {ξ α ∈ T | α ∈ L ≤∞ , |α| ≥ n} and σ : Proof.…”

Section: Proofmentioning

confidence: 99%

“…Proof. To find the action ρ of T on C * (Γ), we consider the one-cocycle c : Γ → R given by c(η, k, ξ) = k analogous to what is done in [11].…”

Section: The C*-algebra Of the Labelled Graph As A Groupoid C*-algebramentioning

confidence: 99%

Groupoid Models for the C*-Algebra of Labelled Spaces

Boava

Castro

Mortari

2019

Bull Braz Math Soc, New Series

View full text Add to dashboard Cite

We define a groupoid from a labelled space and show that it is isomorphic to the tight groupoid arising from an inverse semigroup associated with the labelled space. We then define a local homeomorphism on the tight spectrum that is a generalization of the shift map for graphs, and show that the defined groupoid is isomorphic to the Renault-Deaconu groupoid for this local homeomorphism. Finally, we show that the C*-algebra of this groupoid is isomorphic to the C*-algebra of the labelled space as introduced by Bates and Pask.

show abstract

“…Example 2.2 (Deaconu-Renault groupoids [19,Section 3]). The study of topological groupoids associated with endomorphisms began with the seminal paper of Deaconu [6], and has been extended in various directions. In order to associate a groupoid C * -algebra to a k-graph, Kumjian and Pask [9] began the extension of Deaconu-Renault groupoids to transformations of N k .…”

Section: Preliminariesmentioning

confidence: 99%

Zappa–Szép product groupoids and $$C^*$$ C ∗ -blends

et al. 2016

View full text Add to dashboard Cite

Abstract. We study the external and internal Zappa-Szép product of topological groupoids. We show that under natural continuity assumptions the Zappa-Szép product groupoid isétale if and only if the individual groupoids areétale. In our main result we show that the C * -algebra of a locally compact Hausdorffétale Zappa-Szép product groupoid is a C * -blend, in the sense of Exel, of the individual groupoid C * -algebras. We finish with some examples, including groupoids built from * -commuting endomorphisms, and skew product groupoids.

show abstract

Groupoids Associated with Endomorphisms

Cited by 63 publications

References 0 publications

Inverse semigroup actions on groupoids

Inverse semigroup actions on groupoids

Groupoid Models for the C*-Algebra of Labelled Spaces

Zappa–Szép product groupoids and $$C^*$$ C ∗ -blends

Contact Info

Product

Resources

About