Exactness and Fell bundles with the approximation property over inverse semigroups
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866910238028857344 |
|---|---|
| author | Gao, Changyuan Kranz, Julian |
| author_facet | Gao, Changyuan Kranz, Julian |
| contents | We prove that the reduced cross-sectional algebra of a Fell bundle with the approximation property over an inverse semigroup is exact if and only if the unit fiber of the Fell bundle is exact. This generalizes a recent result of the first-named author for actions of second countable locally compact Hausdorff groupoids on separable $C^*$-algebras. Along the way, we reprove some results of Kwaśniewski--Meyer on Fell bundle ideals. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_07572 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Exactness and Fell bundles with the approximation property over inverse semigroups Gao, Changyuan Kranz, Julian Operator Algebras Primary: 46L05, 46L55, Secondary: 37A15, 37A25 We prove that the reduced cross-sectional algebra of a Fell bundle with the approximation property over an inverse semigroup is exact if and only if the unit fiber of the Fell bundle is exact. This generalizes a recent result of the first-named author for actions of second countable locally compact Hausdorff groupoids on separable $C^*$-algebras. Along the way, we reprove some results of Kwaśniewski--Meyer on Fell bundle ideals. |
| title | Exactness and Fell bundles with the approximation property over inverse semigroups |
| topic | Operator Algebras Primary: 46L05, 46L55, Secondary: 37A15, 37A25 |
| url | https://arxiv.org/abs/2601.07572 |