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A Dixmier-Douady theorem for Fell algebras |
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| Authors: | Astrid an Huef |
| Institution: | a Department of Mathematics and Statistics, University of Otago, Dunedin 9054, New Zealand b Department of Mathematics, University of Nevada, Reno, NV 89557, USA c School of Mathematics and Applied Statistics, University of Wollongong, NSW 2522, Australia |
| 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. |
| Keywords: | Brauer group Dixmier-Douady Extension property Fell algebra Groupoid Sheaf cohomology |
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