A Dixmier-Douady classification for Fell algebras

Details A Dixmier-Douady classification for Fell algebras A Dixmier-Douady classification for Fell algebras

2010-04-11

arxiv.org/abs/1004.1787v2

Journal of Functional Analysis 260 (2011) 1543--1581

Mathematics

Operator Algebras

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

Scientific paper

10.1016/j.jfa.2010.11.011

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.

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