An equivalence theorem for reduced Fell bundle C*-algebras

Abstract

We show that if E is an equivalence of upper semicontinuous Fell bundles B and C over groupoids, then there is a linking bundle L(E) over the linking groupoid L such that the full cross-sectional algebra of L(E) contains those of B and C as complementary full corners, and likewise for reduced cross-sectional algebras. We show how our results generalise to groupoid crossed-products the fact, proved by Quigg and Spielberg, that Raeburn's symmetric imprimitivity theorem passes through the quotient map to reduced crossed products.

17 pages

References in corpus (5)

• Renault's Equivalence Theorem for Groupoid Crossed Products
• A higher category approach to twisted actions on C*-algebras
• Renault's Equivalence Theorem for Reduced Groupoid C*-algebras
• Coactions and Fell bundles
• Equivalence of Fell Systems and their Reduced C*-Algebras

Cited by in corpus (8)

• Nuclearity of semigroup C*-algebras and the connection to amenability
• Localised module frames and Wannier bases from groupoid Morita equivalences
• Toeplitz algebras associated to Endomorphisms of Ore semigroups
• Irreducible Induced Representations of Fell Bundle C*-Algebras
• Amenability for Fell bundles over groupoids
• Equivalence and Exact Groupoids
• Amenability, Nuclearity and Tensor Products of $C^{\ast }$-Algebraic Fell Bundles under the Unified Viewpoint of the Fell-Doran Induced Representation Theory
• The Bridge Lemmas between Equivalent Fell Bundles and its Applications