The Dixmier-Douady classes of certain groupoid C∗-algebras with continuous trace

@article{Ionescu2018TheDC,
  title={The Dixmier-Douady classes of certain groupoid C∗-algebras with continuous trace},
  author={Marius Ionescu and Alex Kumjian and Aidan Sims and Dana P. Williams},
  journal={Journal of Operator Theory},
  year={2018}
}
Given a locally compact abelian group G, we give an explicit formula for the Dixmier-Douady invariant of the C∗-algebra of the groupoid extension associated to a Cech 2-cocycle in the sheaf of germs of continuous G-valued functions. We then exploit the blow-up construction for groupoids to extend this to some more general central extensions of etale equivalence relations. 
View PDF on arXiv
4 Citations

4 Citations

The primitive ideal space of groupoid C^*-algebras for groupoids with Abelian isotropy

We study the topology of the primitive ideal space of groupoid C∗algebras for groupoids with abelian isotropy. Our results include the known results for action groupoids with abelain stabilizers.…

Pushouts of extensions of groupoids by bundles of abelian groups

We analyse extensions $\Sigma$ of groupoids G by bundles A of abelian groups. We describe a pushout construction for such extensions, and use it to describe the extension group of a given groupoid G…

A Mackey Normal Subgroup Analysis for Groupoids

Given a normal subgroup bundle $\mathcal A$ of the isotropy bundle of a groupoid $\Sigma$, we obtain a twisted action of the quotient groupoid $\Sigma/\mathcal A$ on the bundle of group $C^*$-algbras…

Properties Preserved by Groupoid Equivalence

. We show that groupoid equivalence preserves a number of groupoid properties such as properness or the property of being topologically principal.

References

SHOWING 1-10 OF 28 REFERENCES

The Dixmier-Douady class of groupoid crossed products

Abstract We give a formula for the Dixmier-Douady class of a continuous-trace groupoid crossed product that arises from an action of a locally trivial, proper, principal groupoid on a bundle of…

Continuous trace C*-algebras with given Dixmer-Douady class

  • I. RaeburnJoseph L. Taylor
  • Mathematics
    Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics
  • 1985
Abstract We give an explicit construction of a continuous trace C*algebra with prescribed Dixmier-Douady class, and with only finite-dimensional irreducible representations. These algebras often have…

The generalized Effros-Hahn conjecture for groupoids

The generalized Effros-Hahn conjecture for groupoid C * -algebras says that, if G is amenable, then every primitive ideal of the groupoid C*-algebra C * (G) is induced from a stability group. We…

On transformation group *-algebras with continuous trace

In this paper we answer some questions posed by Dana Williams in [19] concerning the problem under which conditions the transformation group C*-algebra C* (G, Q) of a locally compact transformation…

Crossed products of continuous-trace *-algebras by smooth actions

We study in detail the structure of C*-crossed products of the form A> G, where A is a continuous-trace algebra and a is an action of a locally compact abelian group G on A, especially in the case…

Groupoid Cohomology and Extensions

We show that Haefliger's cohomology forétale groupoids, Moore's cohomology for locally compact groups and the Brauer group of a locally compact groupoid are all particular cases of sheaf (oř Cech)…

Dixmier-Douady Classes of Dynamical Systems and Crossed Products

Abstract Continuous-trace C*-algebras A with spectrum T can be characterized as those algebras which are locally Monta equivalent to C0(T). The Dixmier-Douady class δ(A) is an element of the Čech…

Morita Equivalence and Continuous-Trace $C^*$-Algebras

The algebra of compact operators Hilbert $C^*$-modules Morita equivalence Sheaves, cohomology, and bundles Continuous-trace $C^*$-algebras Applications Epilogue: The Brauer group and group actions…

Irreducible representations of groupoid $C^*$-algebras

If G is a second countable locally compact Hausdorff groupoid with Haar system, we show that every representation induced from an irreducible representation of a stability group is irreducible.

Groupoid Cohomology and the Dixmier‐Douady Class

Suppose A is a continuous-trace C*-algebra with spectrum A. (Throughout, unless otherwise stated, all C*-algebras will be assumed to be separable and all topological spaces and groupoids will be…