A Dixmier-Douady classification for Fell algebras
Operator Algebras
2011-11-16 v2
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.
Keywords
Cite
@article{arxiv.1004.1787,
title = {A Dixmier-Douady classification for Fell algebras},
author = {Astrid an Huef and Alex Kumjian and Aidan Sims},
journal= {arXiv preprint arXiv:1004.1787},
year = {2011}
}
Comments
37 pages. v2: updated to correct an oversight in the proof of Lemma 3.2