A Dixmier-Douady classification for Fell algebras

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 the Dixmier-Douady invariant of a Fell algebra A, and to prove our classification theorem.

37 pages. v2: updated to correct an oversight in the proof of Lemma 3.2

References in corpus (2)

• Renault's Equivalence Theorem for Reduced Groupoid C*-algebras
• Tensor products of maximal abelian subalgebras of C*-algebras

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