Timeline for How to define (and compute) the Cartan-Killing form of the group of volume-preserving diffeomorphisms?
Current License: CC BY-SA 4.0
18 events
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| Nov 16, 2018 at 0:03 | history | edited | S.Surace |
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| S Sep 20, 2018 at 17:01 | history | bounty ended | CommunityBot | ||
| S Sep 20, 2018 at 17:01 | history | notice removed | CommunityBot | ||
| Sep 18, 2018 at 21:32 | comment | added | S.Surace | Thanks @Gabe. I know that paper, but I haven't managed to distill something from it that would give a hint regarding this question. Maybe someone else might be able to do so. | |
| Sep 18, 2018 at 19:48 | comment | added | Gabe K | I'm not sure of the answer at all, but the following paper may be relevant to this question. It doesn't really discuss Killing forms much but gives some good computations on the diffeomorphism group. math.toronto.edu/khesin/papers/H1-gafa.pdf | |
| Sep 18, 2018 at 13:00 | history | edited | S.Surace | CC BY-SA 4.0 |
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| Sep 18, 2018 at 13:00 | comment | added | S.Surace | @B K My intuition is that the problem for $\text{vect}(M)$ is probably even harder and the Cartan-Killing form more degenerate in some sense. But if we know how to tackle the divergence-free case then we might be able to generalize it. I quoted the question from Terence Tao, who asked it in the context of incompressible fluid mechanics. | |
| Sep 18, 2018 at 11:47 | comment | added | B K | Why is it important to restrict to divergence-free vector fields? The inner product in the Riemannian case can be defined in the same way for general vector fields. Is it known that this approach leads to problems if one allows the vector fields to have non-zero divergence? | |
| Sep 14, 2018 at 11:44 | history | edited | S.Surace | CC BY-SA 4.0 |
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| Sep 14, 2018 at 10:30 | history | edited | S.Surace | CC BY-SA 4.0 |
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| Sep 13, 2018 at 23:01 | history | edited | S.Surace | CC BY-SA 4.0 |
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| Sep 13, 2018 at 22:52 | comment | added | S.Surace | I do not know. The first step for me would be to understand how the Cartan-Killing form could be defined for such an infinite dimensional Lie algebra. I have checked numerous books on the topic without success. | |
| Sep 12, 2018 at 19:22 | comment | added | Ben McKay | Is it semisimple? Does it have a root system? | |
| Sep 12, 2018 at 16:26 | history | edited | Willie Wong |
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| S Sep 12, 2018 at 15:09 | history | bounty started | S.Surace | ||
| S Sep 12, 2018 at 15:09 | history | notice added | S.Surace | Draw attention | |
| Aug 30, 2018 at 21:00 | history | edited | S.Surace | CC BY-SA 4.0 |
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| Aug 30, 2018 at 14:45 | history | asked | S.Surace | CC BY-SA 4.0 |