Title

A Dixmier-Douady theorem for Fell algebras

Document Type

Journal Article

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.

RIS ID

35042

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Link to publisher version (DOI)

http://dx.doi.org/10.1016/j.jfa.2010.11.011