Every locally compact group is the outer automorphism group of a II$_1$ factor
Fuente:
arXiv
Salvato in:
| Autore principale: | |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866917688101568512 |
|---|---|
| author | Vaes, Stefaan |
| author_facet | Vaes, Stefaan |
| contents | We prove that every locally compact second countable group $G$ arises as the outer automorphism group Out $M$ of a II$_1$ factor, which was so far only known for totally disconnected groups, compact groups and a few isolated examples. We obtain this result by proving that every locally compact second countable group is a centralizer group, a class of Polish groups that arise naturally in ergodic theory and that may all be realized as Out $M$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_20299 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Every locally compact group is the outer automorphism group of a II$_1$ factor Vaes, Stefaan Group Theory Dynamical Systems Operator Algebras We prove that every locally compact second countable group $G$ arises as the outer automorphism group Out $M$ of a II$_1$ factor, which was so far only known for totally disconnected groups, compact groups and a few isolated examples. We obtain this result by proving that every locally compact second countable group is a centralizer group, a class of Polish groups that arise naturally in ergodic theory and that may all be realized as Out $M$. |
| title | Every locally compact group is the outer automorphism group of a II$_1$ factor |
| topic | Group Theory Dynamical Systems Operator Algebras |
| url | https://arxiv.org/abs/2403.20299 |