Timeline for Lyndon–Hochschild–Serre spectral sequence for a non-normal subgroup
Current License: CC BY-SA 3.0
5 events
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| Feb 1, 2015 at 8:21 | comment | added | quinque | Yes, relative cohomology are cohomology of homogenious space! And moreover there is a spectral sequence of a bundle. But I want to get this sequence for arbitrary Lie algebra. Here have to be purely algebraic approach for this. | |
| Feb 1, 2015 at 0:50 | comment | added | Qiaochu Yuan | @quinque: that notion of relative Lie algebra cohomology is a little different. If you think of the cohomology of Lie algebras as an algebraic model of the de Rham cohomology of compact Lie groups $G$, then relative Lie algebra cohomology should be an algebraic model of the de Rham cohomology of homogeneous spaces $G/H$. Of course these can make sense if $H$ is not normal, but for group cohomology we want to compute the cohomology of the delooping of these spaces, and we just can't deloop homogeneous spaces in general. | |
| Jan 31, 2015 at 21:57 | comment | added | quinque | math.ru.nl/~solleveld/scrip.pdf Here you can find a definition of relative Lie algebra cohomology. It is done by means of explicit complex but it is still a way to make sense of such kind of objects. | |
| Jan 31, 2015 at 21:53 | comment | added | quinque | What you said is just that this approach does not work. But I mean something different. I even edited my question, wrote "analog of Lyndon–Hochschild–Serre spectral sequence". | |
| Jan 31, 2015 at 21:41 | history | answered | Qiaochu Yuan | CC BY-SA 3.0 |