Morita Enveloping Fell Bundles

We introduce notions of weak and strong equivalence for non-saturated Fell bundles over locally compact groups and show that every Fell bundle is strongly (resp. weakly) equivalent to a semidirect product Fell bundle for a partial (resp. global) action. Equivalences preserve cross-sectional C ∗ -alg...

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Veröffentlicht in:	Boletim da Sociedade Brasileira de Matemática 2019-03, Vol.50 (1), p.3-35
Hauptverfasser:	Abadie, Fernando, Buss, Alcides, Ferraro, Damián
Format:	Artikel
Sprache:	eng
Schlagworte:	Bundles Bundling Equivalence Mathematical and Computational Physics Mathematics Mathematics and Statistics Theoretical
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Zusammenfassung:	We introduce notions of weak and strong equivalence for non-saturated Fell bundles over locally compact groups and show that every Fell bundle is strongly (resp. weakly) equivalent to a semidirect product Fell bundle for a partial (resp. global) action. Equivalences preserve cross-sectional C ∗ -algebras and amenability. We use this to show that previous results on crossed products and amenability of group actions carry over to Fell bundles.
ISSN:	1678-7544 1678-7714
DOI:	10.1007/s00574-018-0088-6