English

Tensor Products of Fell Bundles over Groups

funct-an 2024-12-12 v3 Operator Algebras

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.

Keywords

Cite

@article{arxiv.funct-an/9712006,
  title  = {Tensor Products of Fell Bundles over Groups},
  author = {Fernando Abadie},
  journal= {arXiv preprint arXiv:funct-an/9712006},
  year   = {2024}
}

Comments

AMS-Latex, 41 pages. Replaces the old preprint Tensor Products of Fell Bundles over Discrete Groups (http://xxx.if.usp.br/abs/funct-an/9712006). In the current work Fell bundles over arbitrary locally compact groups are treated