Timeline for Noncommutative torus as a von Neumann algebra
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 14, 2020 at 18:40 | comment | added | Nik Weaver | Yes, that's it. Thanks! | |
| Aug 14, 2020 at 17:58 | comment | added | Ruy | I guess it follows from Theorem 4 in "Elliott, George A.; Evans, David E., The structure of the irrational rotation C*-algebra, Ann. Math. (2) 138, No. 3, 477-501 (1993)". | |
| Aug 14, 2020 at 15:41 | comment | added | Nik Weaver | I was wondering that too! It's been 20 years since I wrote that comment. I think the reason is because they're all hyperfinite (and there is only one hyperfinite $II_1$ factor). But I really don't remember how we know this ... I will think about it. | |
| Aug 14, 2020 at 14:35 | comment | added | Ruy | I wonder if people know what are the indices of finite index subfactors of this vN algebra. I was ready to guess that these should involve the rotation angle $\theta$, or $\hbar$ in your answer, but I now see that this is wrong. If I am reading it correctly you state in the 2nd paragraph of page 146 of your book that these algebras are all isomorphic to each other for all positive values of $\hbar$ (presumably just the irrational ones). Do you have a reference for this result? | |
| Aug 14, 2020 at 3:34 | history | answered | Nik Weaver | CC BY-SA 4.0 |