Timeline for What is the relationship amongst all the different kinds of spectra?
Current License: CC BY-SA 3.0
17 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 17, 2011 at 20:18 | comment | added | Mikola | @Yemon Choi: That is a good point. I guess, the main reason I suspect that there ought to be a unified concept is that there is at least a number of partial chains of inclusion. It seems to me that there are really two general concepts, namely schemes and representations. One of them works for commutative rings, while the other works for monoid/group algebras but permits non-commutativity. Both of them agree in the suitably simple cases of commutative C* algebras and matrices. It seems like there ought to be a non-commutative concept which is the "pullback" of these two notions... | |
| Jul 17, 2011 at 17:42 | comment | added | Yemon Choi | Mikola, why do you think that they should be building towards the same thing, rather than inspired by similar instincts/urges? | |
| Jul 17, 2011 at 16:52 | answer | added | Benjamin Steinberg | timeline score: 5 | |
| Jul 17, 2011 at 3:40 | comment | added | Mikola | @Mariano Suarez-Alvarez: Ok, how about this: What is the most general, useful notion of a spectrum? In other words, where does all this stuff go? They all seem to be building towards something, but I don't quite grasp what the end picture should be. | |
| Jul 17, 2011 at 3:39 | comment | added | Mikola | @algori: Ah, fair enough. I kind of added those in as an after thought, but you are correct that they aren't much like the other options. | |
| Jul 17, 2011 at 0:45 | answer | added | Qiaochu Yuan | timeline score: 8 | |
| Jul 17, 2011 at 0:42 | comment | added | Mariano Suárez-Álvarez | What is the question, exactly? The one in the title? It would take a few books to answer... Maybe the question could be made more focused in order to turn it into something more answerable? | |
| Jul 17, 2011 at 0:38 | history | edited | Qiaochu Yuan | CC BY-SA 3.0 |
added 11 characters in body
|
| Jul 16, 2011 at 23:29 | comment | added | Benjamin Steinberg | One could add in the spectrum of a Boolean algebra or the spectral theory of lattices. | |
| Jul 16, 2011 at 22:33 | comment | added | algori | Mikola -- all examples that you mention but the last one are related and none of them has anything to do with spectral sequences, as far as I can tell. Finally, neither spectra of rings nor spectral sequences have anything to do with spectra in topology that give rise to generalized cohomology theories. | |
| Jul 16, 2011 at 22:07 | comment | added | Yemon Choi | "Decomposition into primary constituents, out of which the original can be reconstructed" | |
| Jul 16, 2011 at 21:10 | comment | added | user5117 | @Mikola: Sure, I didn't mean to suggest your question was a duplicate or anything, just to give some (semi-)relevant links. | |
| Jul 16, 2011 at 21:07 | comment | added | Mikola | @Artie Pendergast-Smith: Right, I saw those but they applied to the specific cases of homotopy and spectral sequences. For my purposes, I am more interested in a general picture, especially as it applies to non-commutative rings and physical problems. | |
| Jul 16, 2011 at 20:59 | comment | added | user5117 | These questions cover some of the same ground: mathoverflow.net/questions/24090/… mathoverflow.net/questions/17357/… | |
| Jul 16, 2011 at 20:50 | history | edited | Mikola | CC BY-SA 3.0 |
added 261 characters in body; deleted 14 characters in body
|
| Jul 16, 2011 at 20:38 | history | edited | Mikola | CC BY-SA 3.0 |
deleted 25 characters in body; added 80 characters in body
|
| Jul 16, 2011 at 20:29 | history | asked | Mikola | CC BY-SA 3.0 |