Timeline for Infinite number of non-isomorphic von Neumann algebras with property Gamma?
Current License: CC BY-SA 3.0
11 events
| when toggle format | what | by | license | comment | |
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| Sep 19, 2015 at 19:23 | comment | added | Jon Bannon | @Jiang: Indeed it is a very nice theorem, and that is a very nice question! | |
| Sep 19, 2015 at 13:12 | comment | added | Jiang | @JonBannon, Sometimes, big theorems suffer from the same fate as nuclear bombs: once invented, never used. I like this theorem very much. One reason is that it involves three fundamental objects in II$_1$ factors: the hyperfinite II$_1$ factor $R$, the free group factor $L(F_n)$ and tensor product. And many questions on $R\otimes L(F_n)$ is unanswered, e.g., I think it is not known whether there exists a MASA $A$ in $R\otimes L(F_n)$ such that $A$ is a maximal injective subalgebra. I tend to believe no. | |
| Sep 19, 2015 at 5:51 | comment | added | Jon Bannon | @Jiang: That really is a nuclear bomb to kill a fly, though, isn't it? | |
| Sep 18, 2015 at 17:54 | comment | added | Jiang | You can apply Ozawa and Popa's theorem proved in the paper arxiv.org/abs/math/0302240. | |
| Sep 18, 2015 at 12:03 | comment | added | Chris Ramsey | No worries. I'll take a look. | |
| Sep 18, 2015 at 11:23 | comment | added | Jon Bannon | A paywall is keeping me away from the paper, but in McDuff's second paragraph it is outlined: plms.oxfordjournals.org/content/s3-21/3/443.extract If I have a moment I can try to write an answer, but this might take a while. | |
| Sep 17, 2015 at 14:42 | comment | added | Chris Ramsey | @JonBannon You are absolutely correct! I was misreading a later paper. Is it easy to see that these are McDuff factors? Perhaps you could give an answer outlining this or giving a reference. Thanks. | |
| Sep 17, 2015 at 0:43 | comment | added | Jon Bannon | Hi Chris! It is a fact that if you tensor a $II_1$ factor with a factor with property $\Gamma$, the resulting thing has property $\Gamma$. Therefore all of the McDuff factors (in the 1969 paper) have property $\Gamma$, as they tensorially absorb the hyperfinite II_1 factor (which has \Gamma). | |
| Sep 16, 2015 at 23:09 | history | edited | Chris Ramsey | CC BY-SA 3.0 |
Tried to add some context for why people should care about property Gamma.
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| Sep 15, 2015 at 23:34 | history | edited | Chris Ramsey | CC BY-SA 3.0 |
Added a sentence.
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| Sep 15, 2015 at 20:15 | history | asked | Chris Ramsey | CC BY-SA 3.0 |