Every locally compact group is the outer automorphism group of a II$_1$ factor
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866917688101568512 |
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| 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 |