Tensor Products of Fell Bundles over Groups

1997/12/16 by Fernando Abadie, Abadie, Fernando · 3 citations
Mathematics · Medicine · Physics and Astronomy · #Advanced Operator Algebra Research #Advanced Neuroimaging Techniques and Applications #Noncommutative and Quantum Gravity Theories

paper · pdf · doi:10.48550/arxiv.funct-an/9712006

Abstract

We extend the theory of tensor products of C*-algebras to the larger category of Fell bundles over locally compact groups. We prove that, like in the case of C*-algebras, there exist maximal and minimal tensor products. Given two Fell bundles, we compare the tensor products of their cross-sectional algebras with the cross-sectional algebras of their tensor products. As applications we prove that, under certain conditions, the cross-sectional C*-algebra of a Fell bundle is nuclear or exact whenever so is its fiber over the unit element of the group.

Cited by

• Approximation property of C*-algebraic bundles
• Tensor-product coaction functors
• Inverse semigroup C*-algebras associated with left cancellative\n semigroups

Related

• Kernels of Fell bundles tensor products
• Maximality of dual coactions on sectional C*-algebras of Fell bundles\n and applications
• Deformation of Fell bundles
• On Nuclearity of C^*-algebras of Fell bundles over étale groupoids
• Amenability, Nuclearity and Tensor Products of C^∗-Algebraic Fell Bundles under the Unified Viewpoint of the Fell-Doran Induced Representation Theory