Timeline for Mysterious quotes (at least for me)
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
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| Mar 19, 2021 at 17:19 | comment | added | Sebastien Palcoux | Let me mention some new comments of Yemon Choi (about this answer) written in an other post: mathoverflow.net/questions/386464/… | |
| Dec 6, 2014 at 12:31 | history | edited | Sebastien Palcoux | CC BY-SA 3.0 |
I've added a link to the videos of the recent lectures on the modular theory of von Neumann algebras.
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| Nov 24, 2014 at 17:41 | comment | added | Sebastien Palcoux | A cyclic and separating vector $\Omega$ is also called a vacuum or also a bicyclic vector. A factor admits a bicyclic vector, and more generally, see this notes of Serban Stratila (prop. page 2). | |
| Nov 19, 2014 at 8:55 | comment | added | Nicola Ciccoli | Well, at occasions (I was in the audience) Connes by inner time may mean not $\delta$ but the $\Omega$ dependent modular flow $\sigma^\Omega$. This is what happens, for example for the non commutative 2-torus in his work about "modular curvature" | |
| Nov 10, 2014 at 21:24 | comment | added | Sebastien Palcoux | @AndréHenriques, the quote becomes: "a NC algebra creates its own intrinsic one-parameter bimodule". | |
| Nov 10, 2014 at 20:40 | comment | added | André Henriques | I have a comment on the "up to inner automorphisms" part of Sebastien's answer. The automorphism $\sigma^t_\Omega:M\to M$ does depend on $\Omega$, and indeed two different states $\Omega$ and $\Omega'$ produce automorphisms $\sigma^t_\Omega$ and $\sigma^t_{\Omega'}$ that are only equal in $Out(M)$. But there's is a better statement than merely saying that $\sigma^t_\Omega$ and $\sigma^t_{\Omega'}$ become equal in $Out(M)$. The better statement is that the bimodules ${}_MM_{\sigma^t_\Omega,M}$ and ${}_MM_{\sigma^t_{\Omega'},M}$ (where one twists the right actions) are canonically isomorphic. | |
| Nov 10, 2014 at 16:07 | history | edited | Sebastien Palcoux | CC BY-SA 3.0 |
addition of the dense subspace of the Hilbert space + minor edit
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| Nov 8, 2014 at 14:48 | history | edited | Sebastien Palcoux | CC BY-SA 3.0 |
Addition of an introductive sentence + links
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| Nov 8, 2014 at 0:30 | history | edited | Sebastien Palcoux | CC BY-SA 3.0 |
minor edit
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| Nov 7, 2014 at 23:11 | history | answered | Sebastien Palcoux | CC BY-SA 3.0 |