A Dixmier-Douady theorem for Fell algebras

Authors

Astrid An Huef, University of Wollongong
Alexander Kumjian, University of WollongongFollow
Aidan Sims, University of WollongongFollow

RIS ID

35042

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.

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.