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A Dixmier-Douady theorem for Fell algebras
Faculty of Informatics - Papers (Archive)
  • Astrid An Huef, University of Wollongong
  • Alexander Kumjian, University of Wollongong
  • Aidan Sims, University of Wollongong
Publication Date
Publication Details

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

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.
Citation Information
Astrid An Huef, Alexander Kumjian and Aidan Sims. "A Dixmier-Douady theorem for Fell algebras" (2011) p. 1543 - 1581
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