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Journal of Operator Theory

Volume 81, Issue 2, Spring 2019  pp. 273-319.

Equivalence of Fell bundles over groups

Authors:  Fernando Abadie (1), Damian Ferraro (2)
Author institution:(1) Centro de Matematica, Facultad de Ciencias, Universidad de la Republica, Montevideo, 11400, Uruguay
(2) Departamento de Matematica y Estadistica del Litoral, CENUR Litoral Norte, Universidad de la Republica, Salto, 50000, Uruguay

Summary: We give a notion of equivalence for Fell bundles over groups, not necessarily saturated nor separable. 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.

Keywords: Fell bundles, Morita equivalence

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