Tensor Products of Fell Bundles over Groups
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.
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