Submodules of normalisers in groupoid C*-algebras and discrete group coactions
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2022
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866929309724180480 |
|---|---|
| author | Komura, Fuyuta |
| author_facet | Komura, Fuyuta |
| contents | In this paper, we investigate certain submodules in C*-algebras associated to effective étale groupoids. First, we show that a submodule generated by normalizers is a closure of the set of compactly supported continuous functions on some open set. As a corollary, we show that discrete group coactions on groupoid C*-algebras are induced by cocycles of étale groupoids if the fixed point algebras contain C*-subalgebras of continuous functions vanishing at infinity on the unit spaces. In the latter part, we prove the Galois correspondence result for discrete group coactions on groupoid C*-algebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2206_11713 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Submodules of normalisers in groupoid C*-algebras and discrete group coactions Komura, Fuyuta Operator Algebras 20M18, 22A22, 46L05 In this paper, we investigate certain submodules in C*-algebras associated to effective étale groupoids. First, we show that a submodule generated by normalizers is a closure of the set of compactly supported continuous functions on some open set. As a corollary, we show that discrete group coactions on groupoid C*-algebras are induced by cocycles of étale groupoids if the fixed point algebras contain C*-subalgebras of continuous functions vanishing at infinity on the unit spaces. In the latter part, we prove the Galois correspondence result for discrete group coactions on groupoid C*-algebras. |
| title | Submodules of normalisers in groupoid C*-algebras and discrete group coactions |
| topic | Operator Algebras 20M18, 22A22, 46L05 |
| url | https://arxiv.org/abs/2206.11713 |