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arXiv · 1711.02577

Equivalence of Fell bundles over groups

Fernando Abadie·Damián Ferraro
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Abstract

We give a notion of equivalence for Fell bundles over groups, not necessarily saturated nor separable, and show that equivalent Fell bundles have Morita-Rieffel equivalent cross-sectional $C^*$-algebras. Our notion is originated in the context of partial actions and their enveloping actions. The equivalence between two Fell bundles is implemented by a bundle of Hilbert bimodules with some extra structure. Suitable cross-sectional spaces of such a bundle turn out to be imprimitivity bimodules for the cross-sectional $C^*$-algebras of the involved Fell bundles. We show that amenability is preserved under this equivalence and, by means of a convenient notion of internal tensor product between Fell bundles, we show that equivalence of Fell bundles is an equivalence relation.

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Fernando Abadie, Damián Ferraro. 2017-11-07. Equivalence of Fell bundles over groups. https://doi.org/10.7900/jot.2018feb02.2211

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