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A Dixmier-Douady theorem for Fell algebras

Journal Article


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Abstract


  • We generalise the Dixmier–Douady classification of continuous-trace C*-algebras to Fell algebras. To do

    so, we show that C*-diagonals in Fell algebras are precisely abelian subalgebras with the extension property, and use this to prove that every Fell algebra is Morita equivalent to one containing a diagonal subalgebra. We then use the machinery of twisted groupoid C*-algebras and equivariant sheaf cohomology to define an analogue of the Dixmier–Douady invariant for Fell algebras, and to prove our classification theorem.

Authors


  •   An Huef, Astrid (external author)
  •   Kumjian, Alexander (external author)
  •   Sims, Aidan D.

Publication Date


  • 2011

Citation


  • An Huef, A., Kumjian, A. & Sims, A. (2011). A Dixmier-Douady theorem for Fell algebras. Journal of Functional Analysis, 260 (5), 1543-1581.

Scopus Eid


  • 2-s2.0-78650564249

Ro Full-text Url


  • http://ro.uow.edu.au/cgi/viewcontent.cgi?article=2266&context=infopapers&unstamped=1

Ro Metadata Url


  • http://ro.uow.edu.au/infopapers/1249

Number Of Pages


  • 38

Start Page


  • 1543

End Page


  • 1581

Volume


  • 260

Issue


  • 5

Place Of Publication


  • http://www.sciencedirect.com/science/article/pii/S0022123610004477

Abstract


  • We generalise the Dixmier–Douady classification of continuous-trace C*-algebras to Fell algebras. To do

    so, we show that C*-diagonals in Fell algebras are precisely abelian subalgebras with the extension property, and use this to prove that every Fell algebra is Morita equivalent to one containing a diagonal subalgebra. We then use the machinery of twisted groupoid C*-algebras and equivariant sheaf cohomology to define an analogue of the Dixmier–Douady invariant for Fell algebras, and to prove our classification theorem.

Authors


  •   An Huef, Astrid (external author)
  •   Kumjian, Alexander (external author)
  •   Sims, Aidan D.

Publication Date


  • 2011

Citation


  • An Huef, A., Kumjian, A. & Sims, A. (2011). A Dixmier-Douady theorem for Fell algebras. Journal of Functional Analysis, 260 (5), 1543-1581.

Scopus Eid


  • 2-s2.0-78650564249

Ro Full-text Url


  • http://ro.uow.edu.au/cgi/viewcontent.cgi?article=2266&context=infopapers&unstamped=1

Ro Metadata Url


  • http://ro.uow.edu.au/infopapers/1249

Number Of Pages


  • 38

Start Page


  • 1543

End Page


  • 1581

Volume


  • 260

Issue


  • 5

Place Of Publication


  • http://www.sciencedirect.com/science/article/pii/S0022123610004477