Timeline for Families of representations of von Neumann algebras
Current License: CC BY-SA 4.0
17 events
| when toggle format | what | by | license | comment | |
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| Sep 19, 2023 at 11:49 | history | edited | Matthias Ludewig | CC BY-SA 4.0 |
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| Jan 17, 2022 at 15:57 | vote | accept | Matthias Ludewig | ||
| Jan 14, 2022 at 8:27 | history | edited | Matthias Ludewig | CC BY-SA 4.0 |
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| Jan 14, 2022 at 1:49 | answer | added | Narutaka OZAWA | timeline score: 6 | |
| Jan 13, 2022 at 12:02 | comment | added | Matthias Ludewig | Yes, I think so! How do you show this? Can you give an answer containing a proof or a reference? | |
| Jan 13, 2022 at 4:44 | comment | added | Narutaka OZAWA | The map $V(A,H)\to\operatorname{Hom}(A,B(H))$ is open. Is this good enough? | |
| Jan 13, 2022 at 2:27 | comment | added | Nik Weaver | @MatthiasLudewig thank you, that helps a lot. | |
| Jan 13, 2022 at 0:05 | comment | added | Dmitri Pavlov | @MatthewDaws: In the simplest case, the questions asks whether given a continuous path p:[0,1]→Hom(A,B(H)) together with a lift v∈V(A,H) of p(0), we can construct a continuous path q:[0,1]→V(A,H) that lifts p and such that q(0)=v. The general condition asks the same question in continuous families indexed by disks. | |
| Jan 12, 2022 at 21:37 | comment | added | Matthias Ludewig | I added some more about the motivation below the question in the post above. | |
| Jan 12, 2022 at 21:34 | comment | added | Matthias Ludewig | Sorry if I appeared blunt, this was not the intention. If Serre fibration does not mean much to you, you can take it to mean "fiber bundle" or any other kind of fibration. The definition linked by Jon Bannon is the one to use. Or the one on Wikipedia (en.wikipedia.org/wiki/Fibration). | |
| Jan 12, 2022 at 14:21 | comment | added | Nik Weaver | @MatthiasLudwig, if you're asking for help on something and someone asks you to define an unfamiliar term, this is not a great way to respond. BTW Matthew Daws is very active on mathoverflow and solves a lot of hard problems posed here, so you're really not doing yourself a favor by telling him "the question is perfectly sensible" and refusing to provide a definition. | |
| Jan 12, 2022 at 12:51 | comment | added | Jon Bannon | So the definition one should be looking at is found at the following link, or is there a better equivalent condition you are working with? Serre fibrations aren't that familiar to some folks working in vNas. encyclopediaofmath.org/wiki/Serre_fibration | |
| Jan 12, 2022 at 10:41 | comment | added | Matthias Ludewig | I defined two sets and a sujective continuous map between them. I would say that the question whether this map is a Serre fibration is perfectly sensible. I also added something about what I tried in the post above. | |
| Jan 12, 2022 at 10:41 | history | edited | Matthias Ludewig | CC BY-SA 4.0 |
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| Jan 12, 2022 at 9:52 | history | edited | Matthias Ludewig | CC BY-SA 4.0 |
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| Jan 12, 2022 at 9:20 | comment | added | Matthew Daws | As a complete non-expert, I looked up "Serre fibration" on wikipedia, and I have to say I could not make sense of the definition, as applied in this case. Could you say a bit more about what one would need to prove, and where in particular you get stuck? | |
| Jan 12, 2022 at 9:16 | history | asked | Matthias Ludewig | CC BY-SA 4.0 |