Amenability and approximation properties for partial actions and Fell bundles
Resumen:
Building on previous papers by Anantharaman-Delaroche (AD) we introduce and study the notion of AD-amenability for partial actions and Fell bundles over discrete groups. We prove that the cross-sectional C∗-algebra of a Fell bundle is nuclear if and only if the underlying unit fibre is nuclear and the Fell bundle is AD-amenable. If a partial action is globalisable, then it is AD-amenable if and only if its globalisation is AD-amenable. Moreover, we prove that AD-amenability is preserved by (weak) equivalence of Fell bundles and, using a very recent idea of Ozawa and Suzuki, we show that AD-amenabity is equivalent to an approximation property introduced by Exel.
| 2021 | |
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Fell bundles Approximation property Amenability Group actions |
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| Inglés | |
| Universidad de la República | |
| COLIBRI | |
| https://hdl.handle.net/20.500.12008/38420 | |
| Acceso abierto | |
| Licencia Creative Commons Atribución - No Comercial - Sin Derivadas (CC - By-NC-ND 4.0) |
| Sumario: | Publicado también como: Bulletin of the Brazilian Mathematical Society, New Series, 2022, 53: 173–227. DOI: 10.1007/s00574-021-00255-8 |
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