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Amenability and approximation properties for partial actions and Fell bundles
- Publication Year :
- 2019
- Publisher :
- arXiv, 2019.
-
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.<br />Comment: 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
- Subjects :
- Pure mathematics
geography
geography.geographical_feature_category
46L55 (Primary), 46L99 (Secondary)
Approximation property
Mathematics::Operator Algebras
General Mathematics
Fell
Mathematics - Operator Algebras
Action (physics)
If and only if
Bundle
FOS: Mathematics
Algebra over a field
Operator Algebras (math.OA)
Unit (ring theory)
Equivalence (measure theory)
Mathematics
Subjects
Details
- Database :
- OpenAIRE
- Accession number :
- edsair.doi.dedup.....7d3b4740b019beceaae47ea4c6807b57
- Full Text :
- https://doi.org/10.48550/arxiv.1907.03803