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

Journal Article


Abstract


  • 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 Ĉech 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 étale equivalence relations.

UOW Authors


  •   Ionescu, Marius (external author)
  •   Kumjian, Alexander (external author)
  •   Sims, Aidan
  •   Williams, Dana P. (external author)

Publication Date


  • 2019

Citation


  • Ionescu, M., Kumjian, A., Sims, A. & Williams, D. P. (2019). The Dixmier-Douady classes of certain groupoid C*-algebras with continuous trace. Journal of Operator Theory, 81 (2), 407-431.

Scopus Eid


  • 2-s2.0-85066267833

Number Of Pages


  • 24

Start Page


  • 407

End Page


  • 431

Volume


  • 81

Issue


  • 2

Place Of Publication


  • Romania

Abstract


  • 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 Ĉech 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 étale equivalence relations.

UOW Authors


  •   Ionescu, Marius (external author)
  •   Kumjian, Alexander (external author)
  •   Sims, Aidan
  •   Williams, Dana P. (external author)

Publication Date


  • 2019

Citation


  • Ionescu, M., Kumjian, A., Sims, A. & Williams, D. P. (2019). The Dixmier-Douady classes of certain groupoid C*-algebras with continuous trace. Journal of Operator Theory, 81 (2), 407-431.

Scopus Eid


  • 2-s2.0-85066267833

Number Of Pages


  • 24

Start Page


  • 407

End Page


  • 431

Volume


  • 81

Issue


  • 2

Place Of Publication


  • Romania