Amenability and approximation properties for partial actions and Fell bundles
Abstract
Building on previous papers by Anantharaman-Delaroche (AD) we introduce and study the notion of AD-amenability for partial actions and Fell bundles over discrete groups. We prove that the cross-sectional C*-algebra of a Fell bundle is nuclear if and only if the underlying unit fibre is nuclear and the Fell bundle is AD-amenable. If a partial action is globalisable, then it is AD-amenable if and only if its globalisation is AD-amenable. Moreover, we prove that AD-amenability is preserved by (weak) equivalence of Fell bundles and, using a very recent idea of Ozawa and Suzuki, we show that AD-amenabity is equivalent to an approximation property introduced by Exel.
Keywords
Cite
@article{arxiv.1907.03803,
title = {Amenability and approximation properties for partial actions and Fell bundles},
author = {Fernando Abadie and Alcides Buss and Damián Ferraro},
journal= {arXiv preprint arXiv:1907.03803},
year = {2021}
}
Comments
Substantial modifications. A new idea was added to prove that amenability and the AP are equivalent. Appendix was removed, size of the paper was reduced