A universal coefficient theorem for actions of finite groups on C*-algebras
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866911463390576640 |
|---|---|
| author | Meyer, Ralf Nadareishvili, George |
| author_facet | Meyer, Ralf Nadareishvili, George |
| contents | The equivariant bootstrap class in the Kasparov category of actions of a finite group G consists of those actions that are equivalent to one on a Type I C*-algebra. Using a result by Arano and Kubota, we show that this bootstrap class is already generated by the continuous functions on G/H for all cyclic subgroups H of G. Then we prove a Universal Coefficient Theorem for the localisation of this bootstrap class at the group order |G|. This allows us to classify certain G-actions on stable Kirchberg algebras up to cocycle conjugacy. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_11787 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A universal coefficient theorem for actions of finite groups on C*-algebras Meyer, Ralf Nadareishvili, George Operator Algebras K-Theory and Homology Primary 19K35, Secondary 46L35 The equivariant bootstrap class in the Kasparov category of actions of a finite group G consists of those actions that are equivalent to one on a Type I C*-algebra. Using a result by Arano and Kubota, we show that this bootstrap class is already generated by the continuous functions on G/H for all cyclic subgroups H of G. Then we prove a Universal Coefficient Theorem for the localisation of this bootstrap class at the group order |G|. This allows us to classify certain G-actions on stable Kirchberg algebras up to cocycle conjugacy. |
| title | A universal coefficient theorem for actions of finite groups on C*-algebras |
| topic | Operator Algebras K-Theory and Homology Primary 19K35, Secondary 46L35 |
| url | https://arxiv.org/abs/2406.11787 |