The unitary group of a $\mathrm{II}_1$ factor is SOT-contractible
Fuente:
arXiv
Salvato in:
| Autore principale: | |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866912568244699136 |
|---|---|
| author | Jekel, David |
| author_facet | Jekel, David |
| contents | We show that the unitary group of any SOT-separable $\mathrm{II}_1$ factor $M$, with the strong operator topology, is contractible. Combined with several old results, this implies that the same is true for any SOT-separable von Neumann algebra with no type $\mathrm{I}_n$ direct summands ($n < \infty$). The proof for the $\mathrm{II}_1$-factor case uses regularization via free convolution and Popa's theorem on the existence of approximately free Haar unitaries in $\mathrm{II}_1$ factors. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_05834 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The unitary group of a $\mathrm{II}_1$ factor is SOT-contractible Jekel, David Operator Algebras Primary: 46L10, Secondary: 46L54, 55P15 We show that the unitary group of any SOT-separable $\mathrm{II}_1$ factor $M$, with the strong operator topology, is contractible. Combined with several old results, this implies that the same is true for any SOT-separable von Neumann algebra with no type $\mathrm{I}_n$ direct summands ($n < \infty$). The proof for the $\mathrm{II}_1$-factor case uses regularization via free convolution and Popa's theorem on the existence of approximately free Haar unitaries in $\mathrm{II}_1$ factors. |
| title | The unitary group of a $\mathrm{II}_1$ factor is SOT-contractible |
| topic | Operator Algebras Primary: 46L10, Secondary: 46L54, 55P15 |
| url | https://arxiv.org/abs/2508.05834 |