Timeline for lists of computed cohomologies?
Current License: CC BY-SA 2.5
12 events
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| Jul 26, 2010 at 10:21 | comment | added | student | @Mariano Suárez-Alvarez, The point why I put the points 1) - 3) together was simply that for all three objects I am interested in a "list" or an overview of what is known about computed examples. The motivation for this question was that all three cohomologies occur in existence and classification results of what I am studying at the moment (star products, invariant star products, quantum momentum maps...). By the way, if $\mathfrak{G}$ is the Lie-Algebra of a compact Lie-group $G$ the Lie-algebra-cohomology is the same as the Lie-group-cohomology. | |
| Jul 26, 2010 at 10:03 | history | edited | student | CC BY-SA 2.5 |
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| Jul 26, 2010 at 6:07 | comment | added | Sean Tilson | this is also an cool resource neil-strickland.staff.shef.ac.uk/courses/bestiary/bestiary.pdf | |
| Jul 25, 2010 at 23:20 | comment | added | Yemon Choi | Seconding Mariano's comment. For a start, by taking Cartesian products of manifolds one gets (by Kunneth) lots of different possible cohomology groups, but this is somehow an uninteristing "list". As it stands, the first part of the question creates an unfortunate impression of "I want to know about X. Tell me all about X." | |
| Jul 25, 2010 at 21:39 | answer | added | skupers | timeline score: 12 | |
| Jul 25, 2010 at 21:35 | comment | added | Mariano Suárez-Álvarez | I do not understand what is the point of the question? On one hand, the first part is rather different to the second one (which might deserve its own question) On the other hand, the first part is rather too wide: you probably are interested in something more specific that "tell me which cohomologies of which objects have been computed?" | |
| Jul 25, 2010 at 21:30 | comment | added | Mariano Suárez-Álvarez | @Emerton, indeed: those are the two Whitehead lemmas (the purely cohomological arguments can be found in Hilton-Stammbach, for example) | |
| Jul 25, 2010 at 21:28 | answer | added | David E Speyer | timeline score: 5 | |
| Jul 25, 2010 at 21:20 | answer | added | Simon Salamon | timeline score: 3 | |
| Jul 25, 2010 at 20:13 | comment | added | Emerton | I believe that all semi-simple Lie algebras (in char. 0) have vanishing first and second lie-algebra cohomology. (The first cohomology measures exts. of the trivial rep'n by itself, which must split because of semi-simplicity. The second cohomology measures central extensions of the Lie algebra, which must split because of the existence of Levi decompositions.) | |
| Jul 25, 2010 at 20:00 | answer | added | José Figueroa-O'Farrill | timeline score: 1 | |
| Jul 25, 2010 at 19:20 | history | asked | student | CC BY-SA 2.5 |